Action of Hecke operators on products of Igusa theta constants with rational characteristics
Admissible -adic measures attached to triple products of elliptic cusp forms.
Algèbres de Hecke quasi-ordinaires universelles
An odd square as a sum of an odd number of odd squares
Announcement of errors in "The Eichler Commutation Relation for theta series with spherical harmonics" (Acta Arith. 63 (1993), 233-254)
Anticyclotomic main conjectures.
Arithmetic of half integral weight theta-series
Casimir operators on pseudodifferential operators of several variables.
Computing Hecke eigenvalues below the cohomological dimension.
Estimates for eigenvalues of Hecke operators on Siegel cusp forms.
Explicit Hecke series for symplectic group of genus 4
Shimura conjectured the rationality of the generating series for Hecke operators for the symplectic group of genus . This conjecture was proved by Andrianov for arbitrary genus , but the explicit expression was out of reach for genus higher than 3. For genus , we explicitly compute the rational fraction in this conjecture. Using formulas for images of double cosets under the Satake spherical map, we first compute the sum of the generating series, which is a rational fraction with polynomial coefficients....
Hecke eigenvalues for real quadratic fields.
Hecke operators for GLₙ and buildings
Hecke operators on de Rham cohomology.
We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.
Hecke operators on the -analogue of group cohomology.
Interaction sums and action of Hecke operators on theta-series
Lefschetz formulae for arithmetic varieties.
On Dirichlet Series and Petersson Products for Siegel Modular Forms
We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree and weight has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight may be expressed in terms of the residue at of the associated Dirichlet series.
On interaction of Hecke-Shimura rings: symplectic versus orthogonal
On Saito-Kurokawa Descent for congruence subgroups.