Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
A NUMERICAL STUDY OF SIEGEL THETA SERIES OF VARIOUS DEGREES FOR THE 32-DIMENSIONAL EVEN UNIMODULAR EXTREMAL LATTICES
Manabu OURAMichio OZEKI
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2016 Volume 70 Issue 2 Pages 281-314

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Abstract

Erokhin showed that the Siegel theta series associated with the even unimodular 32-dimensional extremal lattices of degree up to three is unique. Later, Salvati Manni showed that the difference of the Siegel theta series of degree four associated with the two even unimodular 32-dimensional extremal lattices is a constant multiple of the square J2 of the Schottky modular form J, which is a Siegel cusp form of degree four and weight eight. In the present paper we show that the Fourier coefficients of the Siegel theta series associated with the even unimodular 32-dimensional extremal lattices of degrees two and three can be computed explicitly, and the Fourier coefficients of the Siegel theta series of degree four for those lattices are computed almost explicitly.

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© 2016 Faculty of Mathematics, Kyushu University
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