On the standard L-function attached to quaternionic modular forms

On Hecke L-functions attached to half-integral weight modular forms

We would like to recall that in the case of Hecke eigenforms on Γ1 non-vanishing results for their Hecke L-functions at an arbitrary point s0 in the critical strip (not on the critical line) have been proved in [4] (cf. also [7]), using holomorphic kernel functions. This method was carried over to the case of half-integral weight in [8], for arbitrary level. However, in this approach for given ...

Vector valued hermitian and quaternionic modular forms

Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms

In this paper, we propose a generalization of the algorithm developed in [4]. Along the way, we also develop a theory of quaternionic M -symbols whose definition bears some resemblance with the classical M -symbols, except for their combinatorial nature. The theory gives a more efficient way to compute Hilbert modular forms over totally fields, especially quadratic fields, and we have illustrat...

On the images of the Galois representations attached to genus 2 Siegel modular forms

We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic. We prove that the images are as large as possible for almost every prime, if the Siegel cusp form is not a Maass spezialform and verifies two easy to check conditions. Mathematics Subject Classific...

A note on the p-adic Galois representations attached to Hilbert modular forms

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41