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Bulletin of the London Mathematical Society Advance Access originally published online on March 18, 2009
Bulletin of the London Mathematical Society 2009 41(3):423-428; doi:10.1112/blms/bdp012
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© 2009 London Mathematical Society

On theta functions of order 4

Yaacov Kopeliovich

MEAG NY
540 Madison Avenue 6th Floor
New York
NY 10022
USA
ykopeliovich@yahoo.com

Christian Pauly

Département de Mathématiques
Université de Montpellier II
Case Courrier 051
Place Eugène Bataillon
34095 Montpellier Cedex 5
France
pauly@math.univ-montp2.fr

Olivier Serman

Laboratoire Paul Painlevé
UMR 8524 du CNRS
Université des Sciences et Technologies de Lille
Cité scientifique
59655 Villeneuve d’Ascq Cedex
France

Received 6 November 2008.

We prove that the fourth powers of theta functions with even characteristics form a basis of the space H0(A, OA(4{vartheta}))+ of even theta functions of order 4 on a principally polarized Abelian variety (A, {vartheta}) without a vanishing theta-null.

2000 Mathematics Subject Classification 14K25 (primary).

The second author was partially supported by the Ministerio de Educación y Ciencia (Spain) through the grant SAB2006-0022.


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