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A theta relation in genus 4

Published online by Cambridge University Press:  22 January 2016

Eberhard Freitag  and
Manabu Oura
Eberhard Freitag
Affiliation:
Mathematisches Institut, Im Neuenheimer Feld 288, D69120, Heidelberg, freitag@mathi.uni-heidelberg.de
Manabu Oura
Affiliation:
Graduate School of Mathematics, Kyushu University, Japan, ohura@math.kyushu-u.ac.jp
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Abstract

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The 2g theta constants of second kind of genus g generate a graded ring of dimension g(g + 1)/2. In the case g ≥ 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 Φ-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.

Keywords

11T7194B0511F4611F27
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 161 , March 2001 , pp. 69 - 83
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

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