On Kummer?like surfaces attached to singularity and modular forms

Modular forms and K3 surfaces

For every known Hecke eigenform of weight 3 with rational eigenvalues we exhibit a K3 surface over Q associated to the form. This answers a question asked independently by Mazur and van Straten. The proof builds on a classification of CM forms by the second author.

On the Defining Equations of Abelian Surfaces and Modular Forms

On “horizontal” Invariants Attached to Quadratic Forms

We introduce series of invariants related to the dimension for quadratic forms over a field, study relationships between them and prove a few results about them. This is the TEX-ing of a manuscript from 1993 entitled Quadratic forms and simple algebras of exponent two. The original manuscript contained an appendix that has appeared in [K3]: I removed it and replaced references to it by referenc...

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 ...

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