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...

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector...

An automorphic function is an automorphic form for which j {\displaystyle j} is the identity. Some facts about factors of automorphy: Every factor of...

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...

Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely...

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...

this process can be done backwards where the automorphic factor in the theta function is in fact the factor of automorphy defining a line bundle on a complex...

composite numbers (76,64,63,1,0) to the Prime in the 63-aliquot tree. an automorphic number in base 10. It is one of two 2-digit numbers whose square, 5,776...

= 1-automorphic number 797,790,928 = number of centered hydrocarbons with 29 carbon atoms 810,810,000 = smallest number with exactly 1000 factors 815...

(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...

In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital...

constructing measures of network similarity: structural equivalence, automorphic equivalence, and regular equivalence. There is a hierarchy of the three...

public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized...

Or a more general factor of automorphy as discussed in Kollár 1995, §5.2. Kollár, János (1995), Shafarevich maps and automorphic forms, M. B. Porter...

equivalence between motivic and automorphic L-functions postulated in the Langlands program can be tested. Automorphic forms realized in the cohomology...

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...

group Sp(4). Borel, Armand (1979), "Automorphic L-functions", in Borel, Armand; Casselman, W. (eds.), Automorphic forms, representations and L-functions...

theory and the Erlangen program, has an impact in number theory via automorphic forms and the Langlands program. There are many approaches to representation...

Haruzo; Ramakrishnan, Dinakar; Shahidi, Freydoon (eds.), Contributions to automorphic forms, geometry, and number theory, Baltimore, MD: Johns Hopkins Univ...

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...

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...

mathematics, the Langlands–Shahidi method provides the means to define automorphic L-functions in many cases that arise with connected reductive groups...

groups are widely used in number theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms. In case G is...

in the structure of vector spaces of modular forms and more general automorphic representations. Mordell (1917) used Hecke operators on modular forms...

counting the number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence...

ISSN 0003-486X, MR 2521118 Section 12.5 of Iwaniec, Henryk, Topics in classical automorphic forms Section 2.3 of Lemmermeyer, Franz, Reciprocity laws: From Euler...

cohomology theory, again; but in general some assumption coming from automorphic representation theory seems required to get the functional equation....

value with respect to known types of lifting of automorphic forms (now more broadly studied as automorphic representations). While this theory is in one...

{\displaystyle L_{C}(s)} by the inverse Mellin transformation must be an automorphic form of dimension −2 of a special type (see Hecke). If so, it is very...

deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic analysis. In 1997, Iwaniec and John Friedlander proved...