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Topics referred to by the same term
Look up automorphic or automorphism in Wiktionary, the free dictionary. Automorphic may refer to Automorphic number, in mathematics Automorphic form, in
Automorphic
Conjectures connecting number theory and geometry
of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by the Canadian mathematician Robert
Langlands_program
Number whose square ends in the same digits
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose
Automorphic_number
Type of generalization of periodic functions in Euclidean space
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G {\displaystyle G} to the complex numbers
Automorphic_form
Mathematical function on a space that is invariant under the action of some group
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient
Automorphic_function
Mathematical concept
In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive
Automorphic_L-function
In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms
Automorphic_factor
Branch of mathematics that studies abstract algebraic structures
theory and the Erlangen program, has an impact in number theory via automorphic forms and the Langlands program. There are many approaches to representation
Representation_theory
Unsolved problem in mathematics
the growth rate of coefficients of modular forms and more generally, automorphic forms. The name of the conjecture comes from Srinivasa Ramanujan, who
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Japanese mathematician (1930–2019)
of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory
Goro_Shimura
1970 mathematics text by Jacquet and Landlands
Automorphic Forms on GL(2) is a mathematics book by H. Jacquet and Robert Langlands (1970) where they rewrite Erich Hecke's theory of modular forms in
Automorphic_Forms_on_GL(2)
Well-formed crystal with easily recognizable sharp faces (and the opposite term)
in the formation of crystals. Euhedral (also known as idiomorphic or automorphic) crystals are those that are well-formed, with sharp, easily recognised
Euhedral_and_anhedral
Semitopological group in abstract algebra
non-archimedean places. Adelic groups provide the natural setting for automorphic forms and automorphic representations. Their basic quotients, such as G ( K ) ∖
Adelic_algebraic_group
constructing measures of network similarity: structural equivalence, automorphic equivalence, and regular equivalence. There is a hierarchy of the three
Similarity_(network_science)
Natural number
composite numbers (76,64,63,41,1,0) to the Prime in the 41-aliquot tree. an automorphic number in base 10. It is one of two 2-digit numbers whose square, 5,776
76_(number)
Mathematician
geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric
Vladimir_Drinfeld
Canadian mathematician
web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received
Robert_Langlands
American mathematician (1942–2012)
2012) was an American mathematician who worked on group representations, automorphic forms, the Siegel–Weil formula, and Langlands L-functions. Rallis received
Stephen_Rallis
American mathematician, working in automorphic forms. He is considered one of the founders of the theory of automorphic representations and their associated
Hervé_Jacquet
Arithmetic Theory of Automorphic Functions, Princeton University Press, 1994. ISBN 0-691-08092-5 Gelbart, Stephen, Automorphic Forms on Adele Groups
Cusp_form
Mathematical formula in harmonic analysis
a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either
Voronoi_formula
Mathematical theorem
geometry, analytic number theory, spectral geometry, and the theory of automorphic forms. In the case of hyperbolic surfaces, it translates information
Selberg_trace_formula
Series representing modular forms
modular group, Eisenstein series can be generalized in the theory of automorphic forms. Let τ {\displaystyle \tau } be a complex number with strictly
Eisenstein_series
Mathematical object
representations of L F {\displaystyle L_{F}} and, in the global case, the cuspidal automorphic representations of GL n ( A F ) {\displaystyle \operatorname {GL} _{n}(\mathbb
Langlands_group
In projective geometry, a bijection between projective spaces that preserves collinearity
are projective linear transformations (also known as homographies) and automorphic collineations. For projective spaces coming from a linear space, the
Collineation
Product of an integer with itself
3066501376, both ending in 376. (The numbers 5, 6, 25, 76, etc. are called automorphic numbers. They are sequence A003226 in the OEIS.) In base 10, the last
Square_number
Natural number
number of primitive polynomials of degree 33 over GF(2) 212,890,625 = 1-automorphic number 214,358,881 = 146412 = 1214 = 118 222,222,222 = repdigit 222,222
100,000,000
Natural number
Wagstaff prime, Jacobsthal prime 2,825,761 = 16812 = 414 2,890,625 = 1-automorphic number 2,922,509 = Markov prime 2,985,984 = 17282 = 1443 = 126 = 1,000
1,000,000
Concept in number theory
theory. Adeles and ideles are also used in Tate's thesis, the theory of automorphic forms, local-global principles, and adelic descriptions of divisors,
Adele_ring
Natural number
(8810), 21 (4421), and 43 (2243). a repdigit in bases 10, 21 and 43. a 2-automorphic number. the smallest positive integer with a Zeckendorf representation
88_(number)
Country in Southeast Asia
2010 Fields Medal for his proof of fundamental lemma in the theory of automorphic forms. Since the establishment of the Vietnam Academy of Science and
Vietnam
Mathematical concept
equivalence between motivic and automorphic L-functions postulated in the Langlands program can be tested. Automorphic forms realized in the cohomology
Shimura_variety
Harish-Chandra, expressing his idea of a kind of reverse engineering of automorphic form theory, from the point of view of representation theory. The discrete
Parabolic_induction
German mathematician (born 1949)
a German mathematician. His research focuses on global analysis and automorphic forms. Werner Müller grew up in the German Democratic Republic (East
Werner_Müller_(mathematician)
Analytic function on the upper half-plane with a certain behavior under the modular group
group and a growth condition. A modular form is a special case of an automorphic form, which are functions defined on Lie groups that transform nicely
Modular_form
American mathematician
Solomon Friedberg (born 1958) is an American mathematician specializing in automorphic forms, representation theory, and number theory. Friedberg received his
Solomon_Friedberg
Canadian mathematician (born 1944)
FRSC FRS (born May 18, 1944) is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He
James_Arthur_(mathematician)
American mathematician
values of L-functions. Stevens’ research specialties are number theory, automorphic forms, and arithmetic geometry. He has authored or edited several books
Glenn_H._Stevens
Natural number
cubes of the first 21 positive integers 54205 = Zeisel number 54688 = 2-automorphic number 54748 = narcissistic number 54872 = 383, palindromic in base 9
50,000
American mathematician (born 1947)
1947) is an American mathematician working in analytic number theory and automorphic forms at Columbia University. Goldfeld received his B.S. degree in 1967
Dorian_M._Goldfeld
Natural number
code of the city in Beverly Hills, 90210 90,625 = the only five-digit automorphic number: 906252 = 8212890625 91,125 = 453 91,144 = Fine number[clarification
90,000
Theorem in abstract algebra
In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital
Fundamental lemma (Langlands program)
Fundamental_lemma_(Langlands_program)
Group controlling representation theory
that automorphic forms are in a sense functorial in the group G, when k is a global field. It is not exactly G with respect to which automorphic forms
Langlands_dual_group
Natural number
polynomial 1,767,263,190 : The 19th Catalan number. 1,787,109,376 : 1-automorphic number 1,801,088,541 = 217 1,804,229,351 = 715 1,808,141,741 : number
1,000,000,000
Natural number
609,443 = 2435 = 325 888,888,888,888 = repdigit 918,212,890,625 = 1-automorphic number 956,722,026,041 = 59th Fibonacci number. 999,999,999,989 = largest
100,000,000,000
Natural number
divisor number 108,968 = number of signed trees with 11 nodes 109,376 = automorphic number 110,880 = 30th highly composite number 111,111 = repunit 111,777
100,000
Natural number
a placeholder in computer programming, see hexspeak. 12,890,625 = 1-automorphic number 12,960,000 = 36002 = 604 = (3·4·5)4, Plato's "nuptial number"
10,000,000
German mathematician (1849–1925)
established a theory of automorphic functions, associating algebra and geometry. Poincaré had published an outline of his theory of automorphic functions in 1881
Felix_Klein
American mathematician
UCLA. His research deals with number theory, arithmetic geometry, and automorphic forms, in particular, Hilbert modular forms and zeta functions of Shimura
Don_Blasius
Type of Dirichlet series associated to number field extensions
of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far, only a small part of such a
Artin_L-function
can be compactly stated as: "Each digit appears once in each group." Automorphic – A property of some Sudokus where the digits (not just their positions)
Glossary_of_Sudoku
Mathematician
professor of mathematics at Tel Aviv University working in number theory and automorphic forms. Soudry was born in 1956. He received his PhD in mathematics from
David_Soudry
Iranian mathematician
Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method. Shahidi
Freydoon_Shahidi
Low-rank isomorphisms in mathematics
important in the structure theory of algebraic groups and in the study of automorphic forms, theta correspondence, and the Langlands program. Over an algebraically
Exceptional isomorphisms of classical groups
Exceptional_isomorphisms_of_classical_groups
This is a list of Lie group topics, by Wikipedia page. See Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary
List_of_Lie_groups_topics
American mathematician
York City) is an American mathematician, specializing in number theory, automorphic forms, and cryptography. Hoffstein graduated with a bachelor's degree
Jeffrey_Hoffstein
Australian mathematician (born 1981)
interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally
Akshay_Venkatesh
Completes the Langlands program for general linear groups over algebraic function fields
groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands
Lafforgue's_theorem
generalized Riemann hypothesis. It states that the non-trivial zeros of all automorphic L-functions lie on the critical line 1 / 2 + i t {\displaystyle 1/2+it}
Grand_Riemann_hypothesis
algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is
Whitehead's_algorithm
Number, approximately 3.14
theta function an automorphic form, which means that it transforms in a specific way. Certain identities hold for all automorphic forms. An example is
Pi
American mathematician
American mathematician who works in the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic analysis, and
Alex_Kontorovich
Korean educator (born 1978)
at the University of California, Berkeley working in number theory, automorphic forms, and the Langlands program. From 1994 to 1996 when he was in Seoul
Sug_Woo_Shin
Israeli mathematician (1929–2009)
algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions. For the last 30 years of his life he suffered
Ilya_Piatetski-Shapiro
Natural number
primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number, 1-automorphic number, Friedman number since 625 = 56−2, one of the two three-digit
600_(number)
Vietnamese math professor (born 1972)
University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad). He is the first
Ngô_Bảo_Châu
Polish-American mathematician (born 1947)
deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic analysis. In 1997, Iwaniec and John Friedlander proved
Henryk_Iwaniec
Mathematician at the University of Minnesota
mathematics at the University of Minnesota working in number theory, automorphic forms, and the Langlands program. In 1958, Jiang was born in the Lucheng
Dihua_Jiang
Natural number
1 40,002,464,776,083 : 33rd Motzkin number 40,081,787,109,376 : 25th automorphic number 42,486,822,491,890 : number of 53-bead necklaces (turning over
10,000,000,000,000
American mathematician
D., Friedberg, S., & Hoffstein, J. (1996). "On some applications of automorphic forms to number theory", Bulletin of the American Mathematical Society
Daniel_Bump
Axiomatic definition of a class of L-functions
elucidation of its properties, including insight into their relationship to automorphic forms and the Riemann hypothesis. The class was defined by Atle Selberg
Selberg_class
trace formula to prove the Jacquet–Langlands correspondence between automorphic forms on GL2 and its twisted forms. The Arthur–Selberg trace formula
Arthur–Selberg_trace_formula
Japanese mathematician
number theory, multiple trigonometric function theory, zeta functions and automorphic forms. He is currently a professor emeritus at Tokyo Institute of Technology
Nobushige_Kurokawa
German mathematician
American Mathematical Society, "for contributions to number theory, automorphic forms, and arithmetic geometry". Bruinier's homepage at the TU Darmstadt
Jan_Hendrik_Bruinier
Type of vector space
and spherical Hecke algebra that arise when modular forms and other automorphic forms are viewed using adelic groups. These play a central role in the
Hecke_algebra
Number used for counting
digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit
Natural_number
French mathematician (1906-1998)
resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up another credited Weil conjecture
André_Weil
Norwegian mathematician (1917–2007)
mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral
Atle_Selberg
In number theory, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin
Artin_conductor
constructing and analytically continuing several important examples of automorphic L-functions. Some authors reserve the term for a special type of integral
Rankin–Selberg_method
Monster and modular connection
the award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex
Monstrous_moonshine
American-Canadian mathematician (born 1941)
American Canadian mathematician who works in representation theory and automorphic forms. He is a professor emeritus at the University of British Columbia
Bill_Casselman
correspondence between automorphic forms on GL2 and its twisted forms, proved by Jacquet and Langlands (1970, section 16) in their book Automorphic Forms on GL(2)
Jacquet–Langlands correspondence
Jacquet–Langlands_correspondence
Natural number
nodes 9,787,184,545,081 : 175th Markov number 9,918,212,890,625 : 24th 1-automorphic number 9,925,594,216,162 : 176th Markov number 9,999,088,822,075 : number
1,000,000,000,000
Functions on special groups related to their matrix representations
coefficients of certain infinite-dimensional unitary representations, automorphic representations of adelic groups. This approach was further developed
Matrix_coefficient
Meromorphic function on the complex plane
denotes the gamma function, π {\displaystyle \textstyle \pi } denotes the automorphic number, and d {\displaystyle \textstyle d} denotes the degree of the
L-function
Conjecture on zeros of the zeta function
be the most general. The grand Riemann hypothesis extends it to all Automorphic L-functions, such as Mellin transforms of Hecke eigenforms. The Riemann
Riemann_hypothesis
Mathematical functions that quantify complexity
binomial coefficient. One of the conditions in the definition of an automorphic form on the general linear group of an adelic algebraic group is moderate
Height_function
Mathematic theory
to the general linear group GL(n) over an algebraic number field and automorphic representations of its adelic group by Roger Godement and Hervé Jacquet
Tate's_thesis
Number divisible only by 1 and itself
digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit
Prime_number
Indian mathematician (born 1960)
Technology Bombay. He is a number theorist known for his work in the areas of automorphic representations and the Gan–Gross–Prasad conjecture. He was the president
Dipendra_Prasad
American mathematician
is an American mathematician. His primary research interests include automorphic representations. He received his PhD degree from the University of Cambridge
Yuval_Flicker
Integer having a non-trivial divisor
digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit
Composite_number
Venezuelan American mathematician
Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms. He is a professor in the Department of Mathematics at the University
Stephen_S._Kudla
Geometric concept of a 2D space with "points at infinity" adjoined
called automorphic collineations. If α is an automorphism of K, then the collineation given by (x0, x1, x2) → (x0α, x1α, x2α) is an automorphic collineation
Projective_plane
Natural number
11-gon with all diagonals drawn. 376 = 23 × 47, pentagonal number, 1-automorphic number, nontotient, refactorable number. 378 = 2 × 33 × 7, 27th triangular
300_(number)
Matsushima–Murakami formula is a generalization giving dimensions of spaces of automorphic forms, introduced by Matsushima & Murakami (1968). Matsushima, Yozô (1967)
Matsushima's_formula
Iterative algorithm on numbers
digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit
Kaprekar's_routine
Theorem in number theory
Mellin transforms of weight 2 modular forms or a product of analogous automorphic L-functions. Eichler, Martin (1954), "Quaternäre quadratische Formen
Eichler–Shimura congruence relation
Eichler–Shimura_congruence_relation
Natural number
divisors of 288 17,596,287,801 = 1326512 = 26013 = 516 18,212,890,625 = 1-automorphic number 18,348,340,127 = logarithmic number. 18,457,556,052 = 28th Pell
10,000,000,000
AUTOMORPHIC
AUTOMORPHIC
AUTOMORPHIC
AUTOMORPHIC
Girl/Female
Muslim
Beautiful
Girl/Female
Irish
Dusky; dark.
Boy/Male
Biblical
Island of the palm-tree.
Boy/Male
Tamil
Light
Girl/Female
Muslim/Islamic
Smile
Boy/Male
Tamil
Narayana Swamy | நாராயணஸà¯à®µà®¾à®®à¯€Â Â
Lord Vishnu, God
Boy/Male
Tamil
Yashovarman | யஷோவரà¯à®®à®¨
Victorious, Glorious, Famous, Successful
Boy/Male
Hindu
Girl/Female
Swedish
Name of a queen.
Girl/Female
Hindu
God has blessed
AUTOMORPHIC
AUTOMORPHIC
AUTOMORPHIC
AUTOMORPHIC
AUTOMORPHIC
n.
Automorphic characterization.
a.
Patterned after one's self.