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December 2011 On Expressions of Theta Series by $\eta$-products
Akihiko OKAMOTO
Tokyo J. Math. 34(2): 319-326 (December 2011). DOI: 10.3836/tjm/1327931388

Abstract

In this paper, we give a certain identity between an $\eta$-product of weight 1 and theta series associated with a pair of binary quadratic forms. We also have explicit description of Siegel's theorem by an $\eta$-product. For quadratic forms $Q_1$ and $Q_2$ which are in the same genus, we express the difference $\vartheta_{Q_1}(\tau)-\vartheta_{Q_2}(\tau)$ by an $\eta$-product.

Citation

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Akihiko OKAMOTO. "On Expressions of Theta Series by $\eta$-products." Tokyo J. Math. 34 (2) 319 - 326, December 2011. https://doi.org/10.3836/tjm/1327931388

Information

Published: December 2011
First available in Project Euclid: 30 January 2012

zbMATH: 1250.11042
MathSciNet: MR2918908
Digital Object Identifier: 10.3836/tjm/1327931388

Subjects:
Primary: 11F11, 11F20

Rights: Copyright © 2011 Publication Committee for the Tokyo Journal of Mathematics

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Vol.34 • No. 2 • December 2011
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