Hermitian modular forms congruent to 1

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...

Congruence of Hermitian Matrices by Hermitian Matrices

Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...

Reduction mod l of Theta Series of Level l n Nils -

It is proved that the theta series of an even lattice whose level is a power of a prime l is congruent modulo l to an elliptic modular form of level 1. The proof uses arithmetic and algebraic properties of lattices rather than methods from the theory of modular forms. The methods presented here may therefore be especially pleasing to those working in the theory of quadratic forms, and they admi...

Vector valued hermitian and quaternionic modular forms

Modular Matrix Models

Inspired by a formal resemblance of certain q-expansions of modular forms and the master field formalism of matrix models in terms of Cuntz operators, we construct a Hermitian onematrix model, which we dub the “modular matrix model.” Together with an N = 1 gauge theory and a special Calabi-Yau geometry, we find a modular matrix model that naturally encodes the Klein elliptic j-invariant, and he...