A characterization of integral elliptic automorphic forms
A combinatorial interpretation of Serre's conjecture on modular Galois representations
We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic , by their counterparts in the theory of modular symbols.
A relative trace formula proof of the Petersson trace formula
Convergence of generalized eigenfunction expansions.
Critical and ramification points of the modular parametrization of an elliptic curve
Let be an elliptic curve defined over with conductor and denote by the modular parametrization:In this paper, we are concerned with the critical and ramification points of . In particular, we explain how we can obtain a more or less experimental study of these points.
Cusp forms and special values of certain Dirichlet series.
Dedekind type sums and Hecke operators
Distinguishing Hecke eigenvalues of primitive cusp forms
Distribution de points sur une sphère
Distribution of the eigenvalues of Hecke operators.
Eigenvalues of Hecke Operators on SL(2,Z).
Einige Anwendungen der Spurformel im Bereich der Modularkorrespondenzen
Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Facteurs -simples de de grande dimension et de grand rang
Fonctions sphériques et opérateurs de Hecke
Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Hecke operators for GLₙ and buildings
Hecke operators in half-integral weight
In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators with prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators ...
Hecke Operators on ... (m).
L-functions attached to Jacobi forms of degree n. Part I. The basic identity.