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arXiv · 2108.09013

Arithmetic over the Gaussian Number Field on a Certain Family of Elliptic Curves with Complex Multiplication

Yoshihiro Ônishi·Fumio Sairaiji
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Abstract

This work is a sequel of a previous work of one of the authors (Y.Ô), which treated certain congruence relation between an elliptic Gauss sum and a coefficient of power series expansion at the origin of the lemniscate sine function. We extend the previous result (in \cite{O}) which concerned only for non-vanishing elliptic Gauss sums. We give new congruence relations between power series coefficients of the lemniscate cosine function, which hold if and only if the corresponding elliptic Gauss sum vanishes.

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Yoshihiro Ônishi, Fumio Sairaiji. 2021-08-20. Arithmetic over the Gaussian Number Field on a Certain Family of Elliptic Curves with Complex Multiplication. https://arxiv.org/abs/2108.09013

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