Arithmetic vector bundles and automorphic forms on Shimura varieties, II
Arithmétique de courbes modulaires
Arithmetisch ganze Differentiale der Modulfunktionenkörper 6. und 7. Stufe
Arithmetische Eigenschaften hyperbolischer Klassen elliptischer Modulgruppen.
Around the Borromean link.
This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.
Artin formalism and heat kernels.
Artin formalism for Selberg zeta functions of co-finite Kleinian groups
Let be a finite-volume quotient of the upper-half space, where is a discrete subgroup. To a finite dimensional unitary representation of one associates the Selberg zeta function . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if is a finite index group extension of in , and is the induced representation, then . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely , for an appropriate...
Artin -functions and normalization of intertwining operators
Artin L-functions and modular forms associated to quasi-cyclotomic fields
Artin's conjecture, Turing's method, and the Riemann hypothesis.
Asymptotic behaviour of supercuspidal characters of -adic
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Asymptotic formulae for partition ranks
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic Formulae for the Coefficients of a Class of Modular Forms.
Asymptotic formulas and generalized Dedekind sums.
Asymptotic formulas for the coefficients of certain automorphic functions
We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions for all integers k,l...
Asymptotic values of modular multiplicities for
We study the irreducible constituents of the reduction modulo of irreducible algebraic representations of the group for a finite extension of . We show that asymptotically, the multiplicity of each constituent depends only on the dimension of and the central character of its reduction modulo . As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.
Atkin-Lehner Operators.
Automorphic forms
Automorphic forms and functions with respect to the Jacobi group.