Congruences in Hermitian Jacobi and Hermitian modular forms

Vector valued hermitian and quaternionic modular forms

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.

Codes over rings, complex lattices and Hermitian modular forms

We introduce the finite ring S2m = Z2m + iZ2m . We develop a theory of self-dual codes over this ring and relate self-dual codes over this ring to complex unimodular lattices. We describe a theory of shadows for these codes and lattices. We construct a gray map from this ring to the ring Z2m and relate codes over these rings, giving special attention to the case when m = 2. We construct various...

Universal binary Hermitian forms

We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.

Signatures of Hermitian Forms

Signatures of quadratic forms over formally real fields have been generalized in [BP2] to hermitian forms over central simple algebras with involution over such fields. This was achieved by means of an application of Morita theory and a reduction to the quadratic form case. A priori, signatures of hermitian forms can only be defined up to sign, i.e., a canonical definition of signature is not p...