On Hermitian modular forms mod p

SIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...

ON THE WEIGHTS OF MOD p HILBERT MODULAR FORMS

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Hodge theory.

Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms

In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...

Hermitian modular forms congruent to 1

For any natural number l and any prime p ≡ 1 (mod 4) not dividing l there is a Hermitian modular form of arbitrary genus n over L := Q[ √ −l] that is congruent to 1 modulo p which is a Hermitian theta series of an OL-lattice of rank p− 1 admitting a fixed point free automorphism of order p. It is shown that also for non-free lattices such theta series are modular forms.

Vector valued hermitian and quaternionic modular forms