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2001 A theta relation in genus 4
Eberhard Freitag, Manabu Oura
Nagoya Math. J. 161: 69-83 (2001).

Abstract

The $2^{g}$ theta constants of second kind of genus $g$ generate a graded ring of dimension $g(g+1)/2$. In the case $g \geq 3$ there must exist algebraic relations. In genus $g = 3$ it is known that there is one defining relation. In this paper we give a relation in the case $g = 4$. It is of degree $24$ and has the remarkable property that it is invariant under the full Siegel modular group and whose $\Phi$-image is not zero. Our relation is obtained as a linear combination of code polynomials of the $9$ self-dual doubly-even codes of length $24$.

Citation

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Eberhard Freitag. Manabu Oura. "A theta relation in genus 4." Nagoya Math. J. 161 69 - 83, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 0987.11035
MathSciNet: MR1820213

Subjects:
Primary: 11F27
Secondary: 11F46, 11T71, 94B99

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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