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...

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...

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...

of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by Robert Langlands (1967, 1970)...

mathematics Automorphic form, in mathematics Automorphic representation, in mathematics Automorphic L-function, in mathematics Automorphism, in mathematics...

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

{\displaystyle k} digits is an automorphic number if n {\displaystyle n} is a fixed point of the polynomial function f ( x ) = x 2 {\displaystyle f(x)=x^{2}}...

Dirichlet L-function Automorphic L-function Modularity theorem Artin conjecture Special values of L-functions Explicit formulae for L-functions Shimizu L-function...

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

ISSN 0012-9593. (online). Harder, G. (1974). "Chevalley Groups Over Function Fields and Automorphic Forms". The Annals of Mathematics. 100 (2). JSTOR: 249–306...

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

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 Parkinson's...

is positive, zero or negative; and the s-maps are inverse functions of automorphic functions for the triangle group 〈p, q, r〉 = Δ(p, q, r). The monodromy...

a century. Throughout his career, he wrote papers on automorphic functions and special functions in pure mathematics as well as on electromagnetism, general...

applies to elliptic curves and elliptic functions; and in fact to curves of genus > 1 and automorphic functions.) The properties of algebraic curves, such...

Armand (1979), "Automorphic L-functions", in Borel, Armand; Casselman, W. (eds.), Automorphic forms, representations and L-functions (Proc. Sympos. Pure...

L-functions, alongside the L-functions associated to automorphic representations. Conjecturally, these two types of global L-functions are actually two descriptions...

reputation. In 1915 Ford published An Introduction to the Theory of Automorphic Functions as Edinburgh Mathematical Tract # 6. Returning to Harvard in 1917...

chain model, the Rényi entropy as a function of α can be calculated explicitly because it is an automorphic function with respect to a particular subgroup...

ISBN 0-89871-420-6, p. 25 Siegel, Carl Ludwig (1942). "Note on automorphic functions of several variables". Annals of Mathematics. Second Series. 43...

especially equations he invented, satisfied by elliptic modular functions and automorphic functions. Klein showed that the modular group moves the fundamental...

the complex-analytic nature of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far...

condition. These are automorphic functions, more precisely, the automorphic functions used in the transformation laws for theta functions. Also, any such map...

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

L-functions other than the Riemann zeta function and the Dirichlet L-functions satisfying the above relations? Indeed, the L-functions of automorphic forms...

monodromy group. 22. Uniformization of analytic relations by means of automorphic functions. 23. Further development of the methods of the calculus of variations...

this form is an elliptic differential of the field of associated automorphic functions. Now, going through these observations backward, is it possible...

and poles) of a Riemann surface. According to Detlef Laugwitz, automorphic functions appeared for the first time in an essay about the Laplace equation...

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...

Representation Theory and Automorphic Functions. Boston: Academic Press. ISBN 0-12-279506-7. Bump, Daniel (1998). Automorphic Forms and Representations...