Maass operators and van der Pol-type identities for Ramanujan's tau function
Nonanalytic automorphic integrals on the Hecke groups
1. Introduction. Since its genesis over a century ago in work of Jacobi, Riemann, Poincar ́e and Klein [Ja29, Ri53, Le64], the theory of automorphic forms has burgeoned from a branch of analytic number theory into an industry all its own. Natural extensions of the theory are to integrals [Ei57, Kn94a, KS96, Sh94], thereby encompassing Hurwitz’s prototype, the analytic weight 2 Eisenstein series [Hu81], and to nonanalytic forms [He59, Ma64, Sel56, ER74, Fr85]. A generalization in both directions...
On arbitrary products of eigenforms
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
On cubic symplectic metaplectic forms.
On Hecke eigenforms of half-integral weight.
On Hecke eigenvalues at primes of the form [g(n)]
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
On products of eigenforms
On Saito-Kurokawa Descent for congruence subgroups.
On the coefficients of Drinfeld modular forms.
On the generation of the coefficient field of a newform by a single Hecke eigenvalue
Let be a non-CM newform of weight . Let be a subfield of the coefficient field of . We completely settle the question of the density of the set of primes such that the -th coefficient of generates the field . This density is determined by the inner twists of . As a particular case, we obtain that in the absence of nontrivial inner twists, the density is for equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions...
On the slopes of the operator acting on overconvergent modular forms
We show that the slopes of the operator acting on 5-adic overconvergent modular forms of weight with primitive Dirichlet character of conductor 25 are given by eitherdepending on and .We also prove that the space of classical cusp forms of weight and character has a basis of eigenforms for the Hecke operators and which is defined over .
On type numbers of split orders of definite quaternion algebras.
Opérateurs de Hecke pour et fractions continues
Nous rappelons que Manin décrit l’homologie singulière relative aux pointes de la courbe modulaire comme un quotient du groupe . En s’appuyant sur des techniques de fractions continues, nous donnons une expression indépendante de d’un relèvement de l’action des opérateurs de Hecke de sur .
Operations and cooperations in elliptic cohomology. I: Generalized modular forms and the cooperation algebra.
Oscillations of Hecke eigenvalues at shifted primes.
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.
Parité des valeurs propres des opérateurs de Hecke.
Quadratic forms and a product-to-sum formula
Quantum variance for Hecke eigenforms
Second order modular forms
Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein.