A few words on the leitmotif of this thesis: The main examples for Hermitian modular forms come from the classical case, from Hermitian Eisenstein series due to Hel Braun [Br3] or from liftings, see Gritsenko, Ikeda, Krieg, and lots of others. Cohen and Resnikoff [CoRe] introduced the method of constructing modular forms via theta-series to the theory of… (More)
This paper classifies the even unimodular lattices that have a structure as a Hermitian O K-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For… (More)
For any natural number and any prime p ≡ 1 (mod 4) not dividing there is a Hermitian modular form of arbitrary genus n over L := Q[ √ −] 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… (More)
When spinning particles, such as electrons and photons, undergo spin-orbit coupling, they can acquire an extra phase in addition to the well-known dynamical phase. This extra phase is called the geometric phase (also known as the Berry phase), which plays an important role in a startling variety of physical contexts such as in photonics, condensed matter,… (More)
We classify the lattices of rank 16 over the Eisenstein integers which are even unimodular Z-lattices (of dimension 32). There are exactly 80 unitary isometry classes.