Hermitian quadratic forms and Hermitian modular forms

On Multivariate Hermitian Quadratic Forms

Quantifier elimination over real closed fields (real QE) is an important area of research for various fields of mathematics and computer science. Though the cylindrical algebraic decomposition (CAD) algorithm introduced by G. E. Collins [4] and improved by many successive works has been considered as the most efficient method for a general real QE problem up to the present date, we may have a m...

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.

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...

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.