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Type of mathematical function
In mathematics, a Dirichlet L-series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s , {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty }{\frac
Dirichlet_L-function
Meromorphic function on the complex plane
generalisations. A Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation, is called an L-series. Fundamental
L-function
Special mathematical function
It is a particular Dirichlet L-function, the L-function for the alternating character of period four. The Dirichlet beta function is defined as β ( s
Dirichlet_beta_function
Type of Dirichlet series associated to number field extensions
In mathematics, Artin L-functions are a type of Dirichlet series defined for finite extensions of number fields, encoding informations about linear representations
Artin_L-function
Function in analytic number theory
in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number
Dirichlet_eta_function
Mathematical conjecture about zeros of L-functions
are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
Mathematical series
Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. Specifically, the Riemann zeta function ζ(s) is the Dirichlet series of the
Dirichlet_series
Generalization of the Riemann zeta function for algebraic number fields
of the Riemann zeta function: they can be defined as a Dirichlet series, have an analytic continuation to a meromorphic function on the complex plane
Dedekind_zeta_function
Theorem on the number of primes in arithmetic sequences
was proved by Dirichlet (1837) with Dirichlet L-series. The proof is modeled on Euler's earlier work relating the Riemann zeta function to the distribution
Dirichlet's theorem on arithmetic progressions
Dirichlet's_theorem_on_arithmetic_progressions
Complex-valued arithmetic function
a complex-valued arithmetic function χ : Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle
Dirichlet_character
Analytic function in mathematics
Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function ζ(s) is a function of a complex
Riemann_zeta_function
Dirichlet beta function Dirichlet L-function Hurwitz zeta function Legendre chi function Lerch transcendent Polylogarithm and related functions: Incomplete
List of mathematical functions
List_of_mathematical_functions
(a)te^{at}}{e^{ft}-1}}} for χ a Dirichlet character with conductor f. The Kubota–Leopoldt p-adic L-function Lp(s, χ) interpolates the Dirichlet L-function with the Euler
P-adic_L-function
Subfield of number theory
on the left-hand side is also L ( 1 ) {\displaystyle L(1)} where L ( s ) {\displaystyle L(s)} is the Dirichlet L-function for the field of Gaussian rational
Special_values_of_L-functions
Mathematical concept
Here y is a real parameter. The Riemann zeta function can be replaced by a Dirichlet L-function of a Dirichlet character χ. The sum over prime powers then
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Concept in mathematical analysis
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n
Dirichlet_kernel
Mathematical concept
representation r of the Langlands dual group LG of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form. They
Automorphic_L-function
Type of character in number theory
generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L-functions larger than Dirichlet L-functions, and a natural setting
Hecke_character
Sum in algebraic number theory
the Gamma function. Such sums are ubiquitous in number theory. They occur, for example, in the functional equations of Dirichlet L-functions, where for
Gauss_sum
Exploring properties of the integers with complex analysis
begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions
Analytic_number_theory
Axiomatic definition of a class of L-functions
Selberg class is an axiomatic definition of a class of L-functions. The members of the class are Dirichlet series which obey four axioms that seem to capture
Selberg_class
Integral of sin(x)/x from 0 to infinity
the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over
Dirichlet_integral
Arithmetic function
all over the prime numbers. Arithmetic function Dirichlet L-function Dirichlet series Multiplicative function Apostol (1976), p. 30 Apostol (1976), p
Completely multiplicative function
Completely_multiplicative_function
Mathematical operation on arithmetical functions
In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory
Dirichlet_convolution
Mathematical function
"Table of Dirichlet L-series and prime zeta modulo functions for small moduli". arXiv:1008.2547 [math.NT]. Weisstein, Eric W. "Prime Zeta Function". MathWorld
Prime_zeta_function
Probability distribution
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ( α ) {\displaystyle \operatorname
Dirichlet_distribution
Function studied by Ramanujan
Sequences. 13: Article 10.7.4. Apostol, Tom M. (1990) [1976]. Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics. Vol. 41
Ramanujan_tau_function
German mathematician (1805–1859)
Johann Peter Gustav Lejeune Dirichlet (/ˌdɪərɪˈkleɪ/; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number
Peter Gustav Lejeune Dirichlet
Peter_Gustav_Lejeune_Dirichlet
Transcendental single-variable function
tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred
Clausen_function
Formal power series
generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every
Generating_function
Function that is discontinuous at rationals and continuous at irrationals
names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused
Thomae's_function
Dunkl–Cherednik operator Dickman–de Bruijn function Peter Gustav Lejeune Dirichlet: Dirichlet function, Dirichlet L-function Engel: Engel expansion Erdélyi Artúr:
List of eponyms of special functions
List_of_eponyms_of_special_functions
Special function in mathematics
the Hurwitz zeta function may be expressed as a linear combination of Dirichlet L-functions and vice versa: The Hurwitz zeta function coincides with Riemann's
Hurwitz_zeta_function
Mathematical form
harmonic functions) and functional analysis, Dirichlet forms generalize the Laplacian (the mathematical operator on scalar fields). Dirichlet forms can
Dirichlet_form
Theorem in analytic number theory
class of modified zeta functions and Dirichlet L-functions that possess exactly the same non-trivial zeros as the Riemann zeta function, but whose Euler products
Grosswald–Schnitzer_theorem
Zeta-like functions approximate arbitrary holomorphic functions
universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate
Zeta_function_universality
Theorem
In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a complex-valued, periodic function f {\displaystyle f} to be equal to the sum
Dirichlet–Jordan_test
Formula in number theory
Dirichlet characters (via class field theory) for some modulus f called the conductor. Therefore all the L(1) values occur for Dirichlet L-functions,
Class_number_formula
Potential counterexample to the generalized Riemann hypothesis
counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these are
Siegel_zero
Fourier series) Dirichlet L-function Dirichlet principle Dirichlet problem (partial differential equations) Dirichlet process Dependent Dirichlet process Hierarchical
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Function which is not continuous at any point of its domain
indicator function of the rational numbers, also known as the Dirichlet function. This function is denoted as 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q}
Nowhere_continuous_function
Conjecture on zeros of the zeta function
also be extended to the L-functions of Hecke characters of number fields. Since Dirichlet L-functions are Hecke L-functions for finite characters, then
Riemann_hypothesis
Second-order partial differential equation
solution to the corresponding Dirichlet problem. The Neumann boundary conditions for Laplace's equation specify not the function φ itself on the boundary of
Laplace's_equation
Method of solution to differential equations
that if L {\displaystyle L} is a linear differential operator, then the Green's function G {\displaystyle G} is the solution of the equation L G = δ ,
Green's_function
Rational number sequence
of Dirichlet L-functions in the same way that Bernoulli numbers are related to special values of the Riemann zeta function. Let χ be a Dirichlet character
Bernoulli_number
function, the special case for the poset of integer divisibility is related as a formal Dirichlet series to the Riemann zeta function. Zeta function of
List_of_zeta_functions
terms of the zeta function. The function δ {\displaystyle \delta } is multiplicative, and since it is bounded by 1, its Dirichlet series converges absolutely
Average order of an arithmetic function
Average_order_of_an_arithmetic_function
Conjectures connecting number theory and geometry
L-functions can be defined in a natural way: Artin L-functions. Langlands' insight was to find the proper generalization of Dirichlet L-functions, which
Langlands_program
Special mathematical function defined as sin(x)/x
integrals Dirichlet integral – Integral of sin(x)/x from 0 to infinity Lanczos resampling – Technique in signal processing List of mathematical functions Shannon
Sinc_function
If there are more items than boxes holding them, one box must contain at least two items
commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the
Pigeonhole_principle
Mathematical conjecture
Erhan Özlük, proved the pair correlation conjecture for some of Dirichlet's L-functions.A.E. Ozluk (1982) The connection with random unitary matrices could
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Concept in number theory
In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Peter Gustav Lejeune Dirichlet, is a measure of the size of
Dirichlet_density
Class of mathematical functions
1017/cbo9780511791246. ISBN 978-0-521-53429-1. Apostol, Tom M. (1976), Modular functions and Dirichlet series in number theory (in German), New York: Springer-Verlag
Weierstrass_elliptic_function
Mathematical theorem
answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive c and L such that, if we denote p(a,d)
Linnik's_theorem
Dirichlet L-functions, and other more general global L-functions. A single statement thus combines statements on the complex zeroes of all Dirichlet L-functions
Weil's_criterion
Functions in mathematics
is Dirichlet's principle, representing harmonic functions in the Sobolev space H 1 ( {\displaystyle H^{1}(} as the minimizers of the Dirichlet energy
Harmonic_function
Unsolved problem in mathematics
Ramanujan L-function. It can be defined as a Dirichlet series for Ramanujan tau function: L ( s , τ ) = ∑ n = 1 ∞ τ ( n ) n s . {\displaystyle L(s,\tau )=\sum
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Identity obeyed by many special functions related to the gamma function
non-principal characters may be given in the form of Dirichlet L-functions. The periodic zeta function is sometimes defined as F ( s ; q ) = ∑ m = 1 ∞ e
Multiplication_theorem
Branch of number theory
theories of L-functions and complex multiplication, in particular. In a couple of papers in 1838 and 1839 Peter Gustav Lejeune Dirichlet proved the first
Algebraic_number_theory
Topics referred to by the same term
L series may refer to: L-function, a meromorphic function Dirichlet L-function, in number theory Artin L-function, a type of Dirichlet series Canon L
L_series
Generalized function whose value is zero everywhere except at zero
Fourier series states that the Dirichlet kernel restricted to the interval [−π,π] tends to a multiple of the delta function as N → ∞. This is interpreted
Dirac_delta_function
missing. Explicit formula (L-function) Riemann–Siegel formula (particular approximate functional equation) "§25.15 Dirichlet -functions on NIST". Weisstein,
Functional equation (L-function)
Functional_equation_(L-function)
Function with a repeating pattern
periodic but possess properties that make them less intuitive. The Dirichlet function, for example, is periodic, with any nonzero rational number serving
Periodic_function
Expression of a function as an infinite sum of simpler functions
of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity. A general Dirichlet series is a
Series_expansion
converted into a simpler expression that more readily exhibits the L-function as a Dirichlet series. The simultaneous combination of an unfolding together
Rankin–Selberg_method
generalized Riemann hypothesis for one Dirichlet L-function affects the location of the zeros of other Dirichlet L-functions. Siegel zero Deuring, M. (1933)
Deuring–Heilbronn_phenomenon
Generative topic model
In natural language processing, latent Dirichlet allocation (LDA) is a generative statistical model that explains how a collection of text documents can
Latent_Dirichlet_allocation
Differential operator in mathematics
are functions that make the Dirichlet energy functional stationary: E ( f ) = 1 2 ∫ U ‖ ∇ f ‖ 2 d x . {\displaystyle E(f)={\frac {1}{2}}\int _{U}\lVert
Laplace_operator
Test for series convergence
In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence
Dirichlet's_test
Function equal to the product of its values on coprime factors
{\displaystyle \tau (n)} : the Ramanujan tau function All Dirichlet characters are completely multiplicative functions, for example ( n / p ) {\displaystyle
Multiplicative_function
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
Modes of vibration in mathematics
(1) is often known as the Dirichlet Laplacian when it is considered as accepting only functions u satisfying the Dirichlet boundary condition. More generally
Dirichlet_eigenvalue
Integer that is a perfect square modulo some integer
a Dirichlet L-function as L ( s ) = ∑ n = 1 ∞ ( n q ) n − s . {\displaystyle L(s)=\sum _{n=1}^{\infty }\left({\frac {n}{q}}\right)n^{-s}.} Dirichlet showed
Quadratic_residue
Mathematical function associated to algebraic varieties
global L-function defined as an Euler product of local zeta functions. Hasse–Weil L-functions form one of the two major classes of global L-functions, alongside
Hasse–Weil_zeta_function
Point to which functions converge in analysis
}}\\0&x{\text{ irrational }}\end{cases}}} (a.k.a., the Dirichlet function) has no limit at any x-coordinate. The function f ( x ) = { 1 for x < 0 2 for x ≥ 0 {\displaystyle
Limit_of_a_function
Type of generalization of periodic functions in Euclidean space
field extensions as Abelian groups. - Specific generalizations of Dirichlet L-functions as class field-theoretic objects. - Generally any harmonic analytic
Automorphic_form
Formula for the sum of an arithmetic function
}{x^{s+1}}}\,dx} and a similar formula for Dirichlet L-functions: L ( s , χ ) = s ∫ 1 ∞ A ( x ) x s + 1 d x {\displaystyle L(s,\chi )=s\int _{1}^{\infty }{\frac
Perron's_formula
Number of integers coprime to and less than n
proof of Dirichlet's theorem on arithmetic progressions. The Dirichlet series for φ(n) may be written in terms of the Riemann zeta function as: ∑ n =
Euler's_totient_function
Infinite sum
{1}{n^{s}}}.} Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if
Series_(mathematics)
American mathematician and professor (born 1973)
"Nonvanishing of quadratic Dirichlet L-functions at s=1/2" arXiv:math/9902163v2 K. Soundararajan, "Moments of the Riemann zeta function" https://annals.math
Kannan_Soundararajan
Method of mathematical integration
continuous functions, including elementary functions, for example polynomials. However, the graphs of other functions, for example the Dirichlet function, do
Lebesgue_integral
is the complex variable traditionally used in Dirichlet series. (For details see Hasse–Weil zeta function.) The global products of Z in the two cases used
Local_zeta_function
Algebraic curve in mathematics
function of a complex variable, L, the Hasse–Weil zeta function of E over Q. This function is a variant of the Riemann zeta function and Dirichlet L-functions
Elliptic_curve
special values of L-functions. Do Siegel zeros exist? Find the value of the De Bruijn–Newman constant. Is Selberg class of Dirichlet series equal to class
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Summability method in physics
series Minakshisundaram–Pleijel zeta function Zeta function (operator) ^ Tom M. Apostol, "Modular Functions and Dirichlet Series in Number Theory", "Springer-Verlag
Zeta_function_regularization
Special mathematical function
Li3(z) The polylogarithm function is defined by a power series in z generalizing the Mercator series, which is also a Dirichlet series in s: Li s ( z
Polylogarithm
for the Dirichlet problem. The function v = ψu lies in H1 0(Ω1) where Ω1 is a region with closure in Ω. If f ∈ C∞ c(Ω) and g ∈ C∞(Ω−) ( L f , g ) =
Sobolev spaces for planar domains
Sobolev_spaces_for_planar_domains
Instantaneous rate of change (mathematics)
of limit. If the function f {\displaystyle f} is differentiable at a {\displaystyle a} , that is if the limit L {\displaystyle L} exists, then this
Derivative
Number of prime factors of a natural number
related summatory functions over so-termed factorial moments of the function ω ( n ) {\displaystyle \omega (n)} . A known Dirichlet series involving ω
Prime_omega_function
Generalizations of the Riemann zeta function
{H}}_{n}^{(c)}}{(n+1)^{b}}}=\zeta (a,b,{\bar {c}})} As a variant of the Dirichlet eta function we define ϕ ( s ) = 1 − 2 ( s − 1 ) 2 ( s − 1 ) ζ ( s ) {\displaystyle
Multiple_zeta_function
function that satisfies the heat equation in the domain (0 < x < L) for boundary conditions of type 1 (Dirichlet) at both boundaries x = 0 and x = L.
Green's_function_number
Mathematical function characterizing set membership
{1} _{A}(x)=\left[\ x\in A\ \right].} For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers
Indicator_function
Vector space of functions in mathematics
introduced them in the 1950s: N. Aronszajn ("Boundary values of functions with finite Dirichlet integral", Techn. Report of Univ. of Kansas 14 (1955), 77–94)
Sobolev_space
French-American mathematician
proof of the Riemann hypothesis for Hecke L-functions, a group even more general than Dirichlet L-functions (which would imply an even more powerful result
Louis_de_Branges_de_Bourcia
Gives conditions for the solvability of quadratic equations modulo prime numbers
quadratic field being the product of the Riemann zeta function and a certain Dirichlet L-function The Jacobi symbol is a generalization of the Legendre
Quadratic_reciprocity
Type of mathematical function
using the Risch algorithm other nonelementary integrals, including the Dirichlet integral and elliptic integral. In elementary real-variable settings such
Elementary_function
Differential calculus on function spaces
problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet's principle. Plateau's
Calculus_of_variations
Theorem in mathematics
mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that if
Inverse_function_theorem
Type of polynomial
polynomials were known in nineteenth-century studies of Dirichlet L-functions, and indeed to Dirichlet himself. They have acquired the name of Michael Fekete
Fekete_polynomial
Four basic unsolved problems about prime numbers
10^{3321634}} assuming the Generalized Riemann hypothesis (GRH) for Dirichlet L-functions. Johnston and Starichkova give a version working for all n ≥ 4 at
Landau's_problems
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
Girl/Female
Muslim
Pl of hazz, Fortune, Good l
Male
French
French form of Hebrew Rephael, RAPHAËL means "healed of God" or "whom God has healed."
Girl/Female
Assamese, British, Gujarati, Hindu, Indian, Kannada, Malay, Malayalam, Marathi, Mythological, Oriya, Sindhi, Tamil
Like a Goddess; Daughter of Shukraacharya; L
Girl/Female
African, Arabic, Australian, Danish, German, Muslim, Pashtun, Swahili
Pure; L; Holy; Clean; Dean
Boy/Male
Indian, Sanskrit
Miner; L Digger
Male
Irish
Irish form of Greek Paulos, PÓL means "small."
Male
Scottish
Scottish form of Latin Paulus, PÀL means "small."
Male
Swedish
Swedish form of Greek Paulos, PÃ…L means "small."
Male
Irish
Irish Gaelic form of Greek MichaÄ“l, MÃCHEÃL means "who is like God?"
Boy/Male
Irish
Rooster.
Boy/Male
Muslim
Lord of majesty and generosity
Boy/Male
Indian
Lord of majesty and generosity
Male
French
French name derived from Latin natalis dies, NOËL means "day of birth."
Male
Hungarian
Hungarian form of Roman Latin Cornelius, KORNÉL means "of a horn."
Girl/Female
Indian
Pl of hazz, Fortune, Good l
Male
Dutch
, God's judge.
Male
French
French form of Greek Ioel (Hebrew Yowel), JOËL means "Jehovah is God" or "to whom Jehovah is God."
Male
French
Masculine form of French Gaëlle, GAËL means "holy and generous."
Male
Hungarian
Hungarian form of Greek Paulos, PÃL means "small."
Male
Norwegian
Norwegian variant form of Scandinavian Njal, NJÃ…L means "champion."
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
Boy/Male
Muslim/Islamic
Name of a prophet
Girl/Female
American, Australian, Chinese, Christian, German
Just; Fairness; Upright; Fair
Surname or Lastname
English
English : from an Old English personal name, either Rǣdweald or Rǣdwulf. The first element in each is rǣd ‘counsel’, ‘advice’; the final elements are weald ‘rule’ and wulf ‘wolf’.English : topographic name, from Old English (ge)ryd(d) ‘cleared’ + weald ‘woodland’, ‘high woodland subsequently cleared’.
Boy/Male
American, British, Christian, Danish, English, French, Gaelic, German, Hindu, Indian, Irish, Italian, Jamaican, Latin, Scandinavian, Tamil
Dark Cloud; Champion; Dark Night; Black
Girl/Female
Muslim
Boy/Male
Muslim
A narrator of Hadith
Boy/Male
British, English
From the Shore Farm
Boy/Male
Indian
Amazing
Girl/Female
Christian & English(British/American/Australian)
Famous
Girl/Female
Muslim
Courageous
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
DIRICHLET L-FUNCTION
v. t.
To betray; to show. [L.]
n.
A symbol representing fifty units, as 50, or l.
n.
The name of the Greek letter /, /, corresponding with the English letter L, l.
n.
See L.
n.
A weed of the genus Lamium (L. amplexicaule) with deeply crenate leaves.
n.
A large stork of the genus Leptoptilos (formerly Ciconia), esp. the African species (L. crumenifer), which furnishes plumes worn as ornaments. The Asiatic species (L. dubius, or L. argala) is the adjutant. See Adjutant.
n.
An extension at right angles to the length of a main building, giving to the ground plan a form resembling the letter L; sometimes less properly applied to a narrower, or lower, extension in the direction of the length of the main building; a wing.
n.
Any small leguminous plant of the genus Lathyrus, especially L. Nissolia.
n.
A short right-angled pipe fitting, used in connecting two pipes at right angles.
n.
An imperfect enunciation of the letter r, in which it sounds like l.
a.
Relating to Casserio (L. Gasserius), the discover of the Gasserian ganglion.
L. catechunenus, Gr.
One who is receiving rudimentary instruction in the doctrines of Christianity; a neophyte; in the primitive church, one officially recognized as a Christian, and admitted to instruction preliminary to admission to full membership in the church.