A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices
type: Item
instance of: scholarly article
title: A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices
zbMATH Open document ID: 1398.11077
author: Michio Ozeki
published in: Tsukuba Journal of Mathematics
publication date: 2017-05-02T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tkbjm/1492104601
review text: It was proved by \textit{R. Salvati Manni} [J. Number Theory 83, No. 2, 282--296 (2000; Zbl 0957.11025)] that the difference of the Siegel theta series of degree \(4\) associated with the two even unimodular extremal lattices of \(48\) dimension is a constant multiple of the cube of the Schottky modular form. This implies that the Siegel theta series of degree \(\leq 3\) is unique. In this paper, the author gives a explicit computation of the Fourier coefficients of the Siegel theta series of degree \(2\) or \(3\) associated with the above mentioned \(48\)-dimensional lattices. Moreover, the author gives an almost explicit computation of the the Fourier coefficients of the Siegel theta series of degree \(4\) for the those lattices.
reviewed by: Atsuhira Nagano
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11E20
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 6710502
zbMATH Keywords: Theta series with spherical functions
zbMATH Keywords: Siegel theta series
zbMATH Keywords: extremal lattices
MaRDI profile type: Publication
OpenAlex ID: W2606857603
DOI: 10.21099/TKBJM/1492104601
description: scientific article; zbMATH DE number 6710502