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December 2016 A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices
Michio Ozeki
Tsukuba J. Math. 40(2): 139-186 (December 2016). DOI: 10.21099/tkbjm/1492104601

Abstract

Salvati Manni showed that the difference of the Siegel theta series of degree 4 associated with the two even unimodular 48-dimensional extremal lattices is a constant multiple of the cube J3 of the Schottky modular form J, which is a Siegel cusp form of degree 4 and weight 8. His result implies that the Siegel theta series of degree up to 3 is unique. But apparently his method does not supply us the process to compute the Fourier coefficients of these series.

In the present paper we show that the Fourier coefficients of the Siegel theta series associated with the even unimodular 48-dimensional extremal lattices of degrees 2 and 3 can be computed explicitly, and the Fourier coefficients of the Siegel theta series of degree 4 for those lattices are computed almost explicitly.

Citation

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Michio Ozeki. "A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices." Tsukuba J. Math. 40 (2) 139 - 186, December 2016. https://doi.org/10.21099/tkbjm/1492104601

Information

Received: 24 June 2016; Revised: 13 October 2016; Published: December 2016
First available in Project Euclid: 13 April 2017

zbMATH: 06710502
MathSciNet: MR3635383
Digital Object Identifier: 10.21099/tkbjm/1492104601

Subjects:
Primary: 11F46
Secondary: 11E20, 11T71

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.40 • No. 2 • December 2016
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