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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
expression appearing in the functional equation of an Artin L-function. Suppose that L {\displaystyle L} is a finite Galois extension of the local field K
Artin_conductor
Meromorphic function on the complex plane
zeta function). Most notably, the mathematicians Bernhard Riemann (1826-1866), Richard Dedekind (1831-1916), Erich Hecke (1887-1947) and Emil Artin (1898-1962)
L-function
Artin. These include Artin's conjecture on primitive roots Artin conjecture on L-functions Artin group Artin–Hasse exponential Artin L-function Artin
List of things named after Emil Artin
List_of_things_named_after_Emil_Artin
Austrian mathematician (1898–1962)
Emil Artin (German: [ˈaʁtiːn]; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians
Emil_Artin
Mathematical theorem
{\displaystyle K} and L {\displaystyle L} . Let: N L / K : C L → C K {\displaystyle N_{L/K}:C_{L}\rightarrow C_{K}} denote idele norm map. The Artin reciprocity
Artin_reciprocity
Generalization of the Riemann zeta function for algebraic number fields
L / K ) {\displaystyle {\text{Gal}}(L/K)} , the resulting Artin L-function is: L ( s , 1 , L / K ) = ζ K ( s ) . {\displaystyle L(s,{\mathcal {1}},L/K)=\zeta
Dedekind_zeta_function
K/k. The S-imprimitive equivariant Artin L-function θ(s) is obtained from the usual equivariant Artin L-function by removing the Euler factors corresponding
Brumer–Stark_conjecture
Artin L-function is a function associated to a finite Galois extension of global fields created by packaging together the various Artin L-functions associated
Equivariant_L-function
Mathematical conjecture about zeros of L-functions
role to Dirichlet L-functions is played by Artin L-functions. Then, ERH is equivalent to Riemann Hypothesis for Artin L-functions. The ERH implies an
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
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
Axiomatic definition of a class of L-functions
case of Artin L-function non-existence of poles violating analictity axiom is subject of Artin conjecture). Another example is the L-function of the modular
Selberg_class
L-functions); and to the global function field case. Here the inclusion of Artin L-functions, in particular, implicates Artin's conjecture; so that the criterion
Weil's_criterion
the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields.
Stark_conjectures
Type of mathematical function
{r}{k}}\right).} Generalized Riemann hypothesis L-function Modularity theorem Artin conjecture Special values of L-functions Dirichlet, Peter Gustav Lejeune (1837)
Dirichlet_L-function
Zeta functions include: Airy zeta function, related to the zeros of the Airy function Arakawa–Kaneko zeta function Arithmetic zeta function Artin–Mazur
List_of_zeta_functions
the L-function L(s, M) of a motive M to L(1 − s, M∨), where M∨ is the dual of the motive M. Basic examples include Artin L-functions and Hasse–Weil L-functions
Motivic_L-function
mathematics, the Artin–Mazur zeta function, named after Michael Artin and Barry Mazur, is a function that is used for studying the iterated functions that occur
Artin–Mazur_zeta_function
Mathematical terminology
formulate the Artin reciprocity law and conjecture what is now called the Artin conjecture concerning the holomorphy of Artin L-functions. Because of the
Galois_representation
Elementary function in mathematics
ρ , s ) = ε ( ρ , s ) L ( ρ v , 1 − s ) {\displaystyle L(\rho ,s)=\varepsilon (\rho ,s)L(\rho ^{v},1-s)} of the Artin L-function associated to ρ {\displaystyle
Langlands–Deligne local constant
Langlands–Deligne_local_constant
Mathematical function
prime zeta function is related to Artin's constant by ln C A r t i n = − ∑ n = 2 ∞ ( L n − 1 ) P ( n ) n {\displaystyle \ln C_{\mathrm {Artin} }=-\sum
Prime_zeta_function
Potential counterexample to the generalized Riemann hypothesis
analytic formulation of quadratic reciprocity (see Artin reciprocity law §Statement in terms of L-functions). The precise relation between the distribution
Siegel_zero
Conjecture on zeros of the zeta function
of Artin L-functions sometimes give rise to multiple zeros of Dedekind zeta functions. Other examples of zeta functions with multiple zeros are the L-functions
Riemann_hypothesis
Z(t)={\frac {1}{(1-t)(1-qt)}}\ .} The first study of these functions was in the 1923 dissertation of Emil Artin. He obtained results for the case of a hyperelliptic
Local_zeta_function
Topics referred to by the same term
mathematics, there are several conjectures made by Emil Artin: Artin conjecture (L-functions) Artin's conjecture on primitive roots The (now proved) conjecture
Artin_conjecture
shortened in Germany and the United States. Cogdell, James (2007). "On Artin L-functions" (PDF). people.math.osu.edu. Ohio State University Department of Mathematics
List of Armenian inventors and discoverers
List_of_Armenian_inventors_and_discoverers
Type of character in number theory
a sense, accounted for by class field theory: their L-functions are Artin L-functions, as Artin reciprocity shows. But even a field as simple as the
Hecke_character
Branch of number theory
corresponds to the Riemann zeta function. When K is a Galois extension, the Dedekind zeta function is the Artin L-function of the regular representation
Algebraic_number_theory
Extension of the factorial function
and Beta functions)". Special Functions. New York: Cambridge University Press. ISBN 978-0-521-78988-2. Artin, Emil (2006). "The Gamma Function". In Rosen
Gamma_function
On the reciprocity law in algebraic number fields
reciprocity involving Artin L-functions and automorphic L-functions: for finite number field extension L / K {\displaystyle L/K} , let ρ {\displaystyle
Hilbert's_ninth_problem
(f^{m})\right|\right)} which is the Artin–Mazur zeta function. The Ihara zeta function is an example of a Ruelle zeta function. List of zeta functions Terras (2010) p. 28
Ruelle_zeta_function
from AG to the abelianization of the Weil group. Abelian extension Artin L-function Artin reciprocity Class field theory Complex multiplication Galois cohomology
Class_formation
varieties See main article arithmetic of abelian varieties Artin L-functions Artin L-functions are defined for quite general Galois representations. The
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Mathematic theory
Artin at Princeton University. In it, Tate used a translation invariant integration on the locally compact group of ideles to lift the zeta function twisted
Tate's_thesis
Fundamental result in the branch of mathematics known as character theory
was application to Artin L-functions. It shows that those are built up from Dirichlet L-functions, or more general Hecke L-functions. Highly significant
Brauer's theorem on induced characters
Brauer's_theorem_on_induced_characters
American mathematician (born 1934)
Michael Artin (German: [ˈaʁtiːn]; born 28 June 1934) is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology
Michael_Artin
Particular kind of exponential sum
a ramified Artin–Schreier covering C, and Weil showed that the local zeta-function of C has a factorization; this is the Artin L-function theory for the
Kloosterman_sum
Artin L-functions. The contemporary formulation of this ambition is by means of the Langlands program: in which grounds are given for believing Artin
Non-abelian class field theory
Non-abelian_class_field_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
Turkish mathematician (1910–1997)
Langlands worked out some arduous calculations on the epsilon factors of Artin L-functions. Arf's portrait is depicted on the reverse of the Turkish 10 lira
Cahit_Arf
Formula in number theory
the theory of Artin L-functions applies to ζ K ( s ) {\displaystyle \zeta _{K}(s)} . It has one factor of the Riemann zeta function, which has a pole
Class_number_formula
Lefschetz fixed-point theorem Artin–Mazur zeta function Ruelle zeta function Fel'shtyn, Alexander (2000), "Dynamical zeta functions, Nielsen theory and Reidemeister
Lefschetz_zeta_function
German mathematician (born 1958)
3-manifold. Following work of Mazur, Deninger (1984) extended Artin–Verdier duality to function fields. Deninger then extended these results in various directions
Christopher_Deninger
Problem about mathematical number fields
extensions of number fields and describe leading coefficients of Artin L-functions. In 2021, Dasgupta and Kakde announced a p-adic solution to finding
Hilbert's_twelfth_problem
Mathematical concept
N L v / K v ( L v × ) → G ab , {\displaystyle \theta _{v}:K_{v}^{\times }/N_{L_{v}/K_{v}}(L_{v}^{\times })\to G^{\text{ab}},} called the local Artin symbol
Global_field
theory analytic number theory Analytic number theory Artin The Artin conjecture says Artin's L function is entire (holomorphic on the entire complex plane)
Glossary_of_number_theory
the Artin–Rees lemma. We denote by P I , M {\displaystyle P_{I,M}} the Hilbert-Samuel polynomial; i.e., it coincides with the Hilbert–Samuel function for
Hilbert–Samuel_function
Complex-valued smooth functions of the upper half plane (harmonic analysis topic)
Friedlander, J. B.; Iwaniec, H. (2002), "The subconvexity problem for Artin L-functions", Inventiones Mathematicae, 149 (3): 489–577, Bibcode:2002InMat.149
Maass_wave_form
French mathematician (born 1962)
class number formula. A conjecture: the Colmez conjecture relating Artin L-functions at s = 0 {\displaystyle s=0} and periods of abelian varieties with
Pierre_Colmez
American mathematician (1925–2019)
"Fourier analysis in number fields and Hecke's zeta functions" under the supervision of Emil Artin. Tate taught at Harvard for 36 years before joining
John_Tate_(mathematician)
Group whose operation is a composition of braids
group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids
Braid_group
Algebraic structure with addition, multiplication, and division
92 Lang (2002), §II.1 Artin (1991), §10.6 Eisenbud (1995), p. 60 Jacobson (2009), p. 213 Artin (1991), Theorem 13.3.4 Artin (1991), Corollary 13.3.6
Field_(mathematics)
Emil Artin conjectures his reciprocity law. 1924 Artin introduces Artin L-functions. 1926 Nikolai Chebotaryov proves his density theorem. 1927 Artin proves
Timeline of class field theory
Timeline_of_class_field_theory
Set of the values of a function
Topological Manifolds, 2nd Ed. Kelley 1985, p. 85 See Munkres 2000, p. 21 Artin, Michael (1991). Algebra. Prentice Hall. ISBN 81-203-0871-9. Blyth, T.S
Image_(mathematics)
Type of zeta function
function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function
Arithmetic_zeta_function
function in p − s {\displaystyle p^{-s}} . Moreover, M. du Sautoy and F. Grunewald showed that the integral can be approximated by Artin L-functions.
Subgroup_growth
On generating functions from counting points on algebraic varieties over finite fields
Grothendieck and Michael Artin managed to construct suitable cohomology theories over the field of ℓ-adic numbers for each prime ℓ ≠ p, called ℓ-adic cohomology
Weil_conjectures
Theorem in complex analysis
treatment of this theorem is in Artin's book The Gamma Function, which has been reprinted by the AMS in a collection of Artin's writings. The theorem was first
Bohr–Mollerup_theorem
Result of repeatedly applying a mathematical function
Iterated functions can be studied with the Artin–Mazur zeta function and with transfer operators. In computer science, iterated functions occur as a
Iterated_function
(1983). "Sous-variétés d'une variété abélienne et points de torsion". In Artin, Michael; Tate, John (eds.). Arithmetic and geometry. Papers dedicated to
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
to parabolic induction. They satisfy a relationship involving Artin L-functions and Artin root numbers when v gives an archimedean local field or when
Langlands–Shahidi_method
British mathematician
two million views. Booker, Andrew R. (2003). "Poles of Artin L-functions and the strong Artin conjecture". Annals of Mathematics. 158 (3): 1089–1098.
Andrew_Booker_(mathematician)
Mathematical conjectures in class field theory
preserve L-functions and ε-factors of pairs of representations, and coincide with the Artin map for 1-dimensional representations. In other words, L(s,ρπ⊗ρπ')
Local_Langlands_conjectures
related to the Artin map. Let L/K be a finite abelian extension of non-archimedean local fields. The conductor of L/K, denoted f ( L / K ) {\displaystyle
Conductor (class field theory)
Conductor_(class_field_theory)
Equation in Fourier analysis
s_{P}(x)} converges in L 1 {\displaystyle L^{1}} norm to an L 1 ( [ 0 , P ] ) {\displaystyle L^{1}([0,P])} function which is periodic on R {\displaystyle
Poisson_summation_formula
Type of a dynamical billiard first studied by Emil Artin in 1924
In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924. It describes the geodesic motion
Artin_billiard
Branch of algebraic number theory concerned with abelian extensions
generalized to the so called Artin reciprocity law; in the idelic language, writing CF for the idele class group of F, and taking L to be any finite abelian
Class_field_theory
Generalization of algebraic spaces or schemes
are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of
Algebraic_stack
36 mathematical problems stated in 1955
attended by international mathematicians including Jean-Pierre Serre, Emil Artin, Andre Weil, Richard Brauer, K. G. Ramanathan, and Daniel Zelinsky The reference
Taniyama's_problems
Type of generalization of periodic functions in Euclidean space
from the idele class group under the Artin reciprocity law. Herein, the analytical structure of its L-function allows for generalizations with various
Automorphic_form
Field in mathematics similar to the real numbers
numbers is the field R a l g {\displaystyle \mathbb {R} _{\mathrm {alg} }} of real algebraic numbers. The theorem is named for Emil Artin and Otto Schreier,
Real_closed_field
Infinite products of functions indexed by primes
\prod _{p}\left(1-{\frac {1}{\left(p+1\right)^{2}}}\right)=0.775883...} Artin's constant OEIS: A005596: ∏ p ( 1 − 1 p ( p − 1 ) ) = 0.373955... {\displaystyle
Euler_product
Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands program modularity theorem Pythagorean
List_of_number_theory_topics
Field theory theorem
elements and his modern version Theorem of the intermediate fields. Emil Artin reformulated Galois theory in the 1930s without relying on primitive elements
Primitive_element_theorem
Sheaf cohomology on the étale site
soon after worked out by Grothendieck together with Michael Artin, and published as (Artin 1962) and SGA 4. Grothendieck used étale cohomology to prove
Étale_cohomology
Mathematical function
is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers. If G is any group, then the
Character_(mathematics)
British mathematician
of algebraic integers to the behaviour of certain analytic functions called Artin L-functions. More recently his research has led him to study various aspects
Martin_J._Taylor
Mathematical connection between field theory and group theory
within F is the field L of symmetric rational functions in the {xα}. The Galois group of F/L is S, by a basic result of Emil Artin. G acts on F by restriction
Galois_theory
Approximation for factorials
2012-03-01 Artin, Emil (2015), The Gamma Function, Dover, p. 24 Toth, V. T. Programmable Calculators: Calculators and the Gamma Function (2006) Archived
Stirling's_approximation
Mathematical law, a generalization of quadratic reciprocity
ideles, the Artin reciprocity law for a finite extension L/K states that the Artin map from the idele class group CK to the abelianization Gal(L/K)ab of the
Reciprocity_law
Concept in class field theory
denotes the commutator subgroup). For more details about Weil groups see (Artin & Tate 2009) or (Tate 1979) or (Weil 1951). The Weil group of a class formation
Weil_group
the Artin L-Functions (PDF). pp. 1–287. Deligne, Pierre (1972). "Les constantes des équations fonctionelles des fonctions L" (PDF). Modular Functions of
Waldspurger_formula
American mathematician
subconvexity problem for Artin L-functions, Inventiones Mathematicae, 149, 489–577. W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc
William_Duke_(mathematician)
Algebraic variety
quartic threefolds are irrational, though some of them are unirational. Artin & Mumford (1972) found some unirational 3-folds with non-trivial torsion
Rational_variety
Number, approximately 3.14
ISBN 3-540-41160-7. Bronshteĭn & Semendiaev 1971, pp. 191–192. Artin, Emil (1964). The Gamma Function. Athena series; selected topics in mathematics (1st ed.)
Pi
ISBN 9781420035223. Frei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (2014). Emil Artin and Helmut Hasse: The Correspondence 1923-1958. Springer Science & Business
List_of_conjectures
Artin reciprocity Local class field theory Iwasawa theory Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem Euler system p-adic L-function
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Theorem in complex analysis
Bibcode:2002math......6203G, ISBN 978-2-85629-141-2, MR 2017446 M. Artin, A. Grothendieck, J.-L. Verdier, SGA 4, Théorie des topos et cohomologie étale des schémas
Riemann's_existence_theorem
Book about number theory
Nakayama, Weil, Artin, and Tate during the period 1950–1952. Alongside the desire to consider algebraic number fields alongside function fields over finite
Basic_Number_Theory
Israeli mathematician and professor
"p-Adic L-functions for Elliptic Curves over CM Fields" under his advisor Barry Mazur from Harvard University, and his mentors Michael Artin and Daniel
Shai_Haran
Mathematical concept
algebraically closed fields, Artin supersingularity implies Shioda supersingularity. The converse — whether Shioda supersingularity implies Artin supersingularity
Supersingular_variety
American mathematician (born 1953)
Freydoon Shahidi, T.-L. Tsai: On Stability of Root Numbers. L {\displaystyle L} -functions and non-abelian class field theory, from Artin to Langlands. In:
James_Cogdell
American mathematician and Nobel Laureate (1928–2015)
algebraic geometry. Nash's theorem itself was famously applied by Michael Artin and Barry Mazur to the study of dynamical systems, by combining Nash's polynomial
John_Forbes_Nash_Jr.
Deformation of the group algebra of a Coxeter group
of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan
Iwahori–Hecke_algebra
Isomorphism of projective spaces in geometry
connection with the function ax + b/cx + d", Messenger of Mathematics 9:104 H. S. M. Coxeter, On periodicity in Mathematical Reviews Artin, E. (1957), Geometric
Homography
Equalities for combinations of sets
\setminus :} L ∩ X = L = X ∩ L where L ⊆ X L ∪ ∅ = L = ∅ ∪ L L △ ∅ = L = ∅ △ L L ∖ ∅ = L {\displaystyle {\begin{alignedat}{10}L\cap X&\;=\;&&L&\;=\;&X\cap
List of set identities and relations
List_of_set_identities_and_relations
Function in algebra
such), the residue field kv = Rv/mv. The concept was developed by Emil Artin in his book Geometric Algebra writing the group in multiplicative notation
Valuation_(algebra)
American mathematician (1895–1973)
JSTOR 1989023. Walsh, J. L. (1933). "Notes on the location of the critical points of Green's function". Bull. Amer. Math. Soc. 39 (10): 775–782
Joseph_L._Walsh
Generalization of algebraic variety
sheaves of categories. From this general notion, Artin defined the narrower class of algebraic stacks (or "Artin stacks"), which can be considered geometric
Scheme_(mathematics)
German mathematician
groups, and L-functions. He has written essays on the history of mathematics, for example, about Helmut Hasse, Hermann Minkowski, and Emil Artin. In 1987
Joachim_Schwermer
ARTIN L-FUNCTION
ARTIN L-FUNCTION
Male
Hungarian
Hungarian form of Greek Paulos, PÃL means "small."
Male
Scottish
Scottish form of Latin Paulus, PÀL means "small."
Male
Norwegian
Norwegian variant form of Scandinavian Njal, NJÃ…L means "champion."
Male
Hungarian
Hungarian form of Roman Latin Cornelius, KORNÉL means "of a horn."
Male
English
English pet form of Celtic Arthur, possibly ARTIE means "bear-man."Â
Male
German
German name derived from Latin Arminius, ARMIN means "army man."
Male
French
French name derived from Latin natalis dies, NOËL means "day of birth."
Male
Swedish
Swedish form of Greek Paulos, PÃ…L means "small."
Male
French
Masculine form of French Gaëlle, GAËL means "holy and generous."
Surname or Lastname
English
English : regional name for someone from the French province of Artois, from Anglo-Norman French Arteis (from Latin Atrebates, the name of the local Gaulish tribe).French : from Old French artis ‘woodworm’, Old Occitan arta ‘moth’, possibly applied as a nickname for someone suffering from a wasting disease, perhaps leprosy.
Male
French
French form of Greek Ioel (Hebrew Yowel), JOËL means "Jehovah is God" or "to whom Jehovah is God."
Boy/Male
Australian, Farsi
Name of a Medes King; Righteous
Male
English
Possibly a variant spelling of English Irvin, ARVIN means "fresh water" or "green water."
Male
French
French form of Hebrew Rephael, RAPHAËL means "healed of God" or "whom God has healed."
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
Irish
Irish form of Greek Paulos, PÓL means "small."
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
English
Variant spelling of English Aaron, ARIN means "light-bringer."Â Compare with feminine Arin.
Male
Irish
Irish Gaelic form of Greek MichaÄ“l, MÃCHEÃL means "who is like God?"
Female
English
Variant spelling of English Erin, ARIN means "Ireland." Compare with masculine Arin.
ARTIN L-FUNCTION
ARTIN L-FUNCTION
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Donation to God
Boy/Male
Australian, French, German, Greek, Italian, Latin
Valiant; Strong; Healthy
Girl/Female
Tamil
Shlaghya | à®·à¯à®²à®¾à®•à¯à®¯à®¾
Excellent
Boy/Male
Hindu, Indian
Gods Name for Success
Boy/Male
Indian, Sanskrit
One who Moves in the Sky
Boy/Male
Tamil
Ornament, Decoration
Girl/Female
Gujarati, Hindu, Indian
Breeze
Boy/Male
Hindu
King of the earth
Male
French
French form of Welsh Arthfael, Old Breton Arthmael, ARMEL means "bear chief" or "warrior prince."
Boy/Male
Hindu, Indian, Tamil
Strong; Growing Up
ARTIN L-FUNCTION
ARTIN L-FUNCTION
ARTIN L-FUNCTION
ARTIN L-FUNCTION
ARTIN L-FUNCTION
n.
A genus of swallows including the purple martin. See Martin.
n.
The name of the Greek letter /, /, corresponding with the English letter L, l.
n.
The European house martin.
n.
A short right-angled pipe fitting, used in connecting two pipes at right angles.
n.
The martin.
n.
A perforated stone-faced runner for grinding.
n.
One of several species of swallows, usually having the tail less deeply forked than the tail of the common swallows.
n.
Any small leguminous plant of the genus Lathyrus, especially L. Nissolia.
n.
A bird. See Martin.
n.
See L.
n.
A symbol representing fifty units, as 50, or l.
n.
The sand martin, or bank swallow.
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.
The feast of St. Martin, the eleventh of November; -- often called martlemans.
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.
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.
v. t.
To betray; to show. [L.]