Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 40, Number 2 (2016), 139-186.
A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices
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.
Tsukuba J. Math., Volume 40, Number 2 (2016), 139-186.
Received: 24 June 2016
Revised: 13 October 2016
First available in Project Euclid: 13 April 2017
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 11T71: Algebraic coding theory; cryptography
Ozeki, Michio. A numerical study of Siegel theta series of various degrees for the 48-dimensional even unimodular extremal lattices. Tsukuba J. Math. 40 (2016), no. 2, 139--186. doi:10.21099/tkbjm/1492104601. https://projecteuclid.org/euclid.tkbjm/1492104601