ON THE CLASSIFICATION OF EVEN UNIMODULAR LATTICES WITH A COMPLEX STRUCTURE-Reference-Cited by-同舟云学术

ON THE CLASSIFICATION OF EVEN UNIMODULAR LATTICES WITH A COMPLEX STRUCTURE

Published:2012-05-16 Issue:04 Volume:08 Page:983-992
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

HENTSCHEL MICHAEL¹,KRIEG ALOYS¹,NEBE GABRIELE²

Affiliation:

1. Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany

2. Lehrstuhl D für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany

Abstract

This paper classifies the even unimodular lattices that have a structure as a Hermitian [Formula: see text]-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 arbitrary imaginary quadratic fields we derive a mass formula for the principal genus of theta lattices which is applied to show completeness of the classifications.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112500583

Reference21 articles.

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