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...

Look up automorphic or automorphism in Wiktionary, the free dictionary. Automorphic may refer to Automorphic number, in mathematics Automorphic form, in mathematics...

1970). It seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and...

automorphic form is a function whose divisor is invariant under the action of G {\displaystyle G} . The factor of automorphy for the automorphic form...

packing, and string theory. Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie...

introduced by Petersson (1930), is a generalization to other modular forms or automorphic forms. The Riemann zeta function and the Dirichlet L-function satisfy...

In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the...

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

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...

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...

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 from...

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

Arithmetic Theory of Automorphic Functions, Princeton University Press, 1994. ISBN 0-691-08092-5 Gelbart, Stephen, Automorphic Forms on Adele Groups, Annals...

mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional elliptic modular forms which are closely related to...

can be tested. Automorphic forms realized in the cohomology of a Shimura variety are more amenable to study than general automorphic forms; in particular...

pair over the completion F ν {\displaystyle F_{\nu }} . Let m be an automorphic form over G, then its H-period splits as a product of local factors (i.e...

transformation must be an automorphic form of dimension −2 of a special type (see Hecke). If so, it is very plausible that this form is an ellipic differential...

field of algebraic topology, and is further credited with introducing automorphic forms. He also made important contributions to algebraic geometry, number...

theta function an automorphic form, which means that it transforms in a specific way. Certain identities hold for all automorphic forms. An example is θ...

ISSN 0025-5831, JFM 15.0351.01, S2CID 120465625 Kra, Irwin (1972), Automorphic forms and Kleinian groups, Mathematics Lecture Note Series, W. A. Benjamin...

decompositions Real form (Lie theory) Complex Lie group Complexification (Lie group) Simple Lie group Compact Lie group, Compact real form Semisimple Lie 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...

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) using...

web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received...

groups. Academic Press. Lax & Phillips 1980 Borel, Armand (1997). Automorphic forms on SL2(R). Cambridge Tracts in Mathematics. Vol. 130. Cambridge University...

^{*}} which follow the cocycle condition. These are automorphic functions, more precisely, the automorphic functions used in the transformation laws for theta...

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...

Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either side...

In mathematics, an Igusa group or Igusa subgroup is a subgroup of the Siegel modular group defined by some congruence conditions. They were introduced...

generalization of the Siegel upper half space Siegel modular form, a type of automorphic form defined on the Siegel upper half-space Siegel modular variety...