Analogues of Jacobi's derivative formula

Kazuhide Matsuda

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arXiv · 1411.3361

Analogues of Jacobi's derivative formula

Kazuhide Matsuda

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Abstract

In this paper, we obtain analogues of Jacobi's derivative formula in terms of the theta constants with rational characteristics. For this purpose, we use the arithmetic formulas of the number of representations of a natural number $n,\,\,(n=1,2,\ldots)$ as the sum of two squares, or the sum of a square and twice a square.

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Kazuhide Matsuda. 2014-10-21. Analogues of Jacobi's derivative formula. https://arxiv.org/abs/1411.3361

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