Analogues of Jacobi's derivative formula

Published 21 Oct 2014 in math.NT | (1411.3361v1)

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

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