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
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
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