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2019 | OriginalPaper | Chapter

5. Theta Series and Even Unimodular Lattices

Authors : Gaëtan Chenevier, Jean Lannes

Published in: Automorphic Forms and Even Unimodular Lattices

Publisher: Springer International Publishing

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Abstract

Most of this chapter may be read independently. We first recall known properties of the Siegel theta series of even unimodular lattices in rank 16 (Witt, Igusa, Kneser) and 24 (Erokhin, Borcherds, Nebe-Venkov…). Then we give two proofs of Theorem A of the introduction (the p-neighbor problem in dimension 16): a short one relying on a construction of Ikeda, and a self-contained one based on a novel use of the triality principle. Along the way, we provide several elementary constructions of orthogonal modular forms, and simple instances of the Eichler commutation relations.

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previous chapter Automorphic Forms and Hecke Operators

next chapter Langlands Parametrization

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Title: Theta Series and Even Unimodular Lattices
Authors: Gaëtan Chenevier
Jean Lannes
Publisher: Springer International Publishing
Book: Automorphic Forms and Even Unimodular Lattices
Print ISBN: 978-3-319-95890-3

Electronic ISBN: 978-3-319-95891-0

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-95891-0_5

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