## Tokyo Journal of Mathematics

### On Expressions of Theta Series by $\eta$-products

Akihiko OKAMOTO

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 34, Number 2 (2011), 319-326.

Dates
First available in Project Euclid: 30 January 2012

https://projecteuclid.org/euclid.tjm/1327931388

Digital Object Identifier
doi:10.3836/tjm/1327931388

Mathematical Reviews number (MathSciNet)
MR2918908

Zentralblatt MATH identifier
1250.11042

#### Citation

OKAMOTO, Akihiko. On Expressions of Theta Series by $\eta$-products. Tokyo J. Math. 34 (2011), no. 2, 319--326. doi:10.3836/tjm/1327931388. https://projecteuclid.org/euclid.tjm/1327931388

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