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

2021/08/20 by Yoshihiro Ônishi, Ônishi, Yoshihiro, Fumio Sairaiji +1
Mathematics · #11G05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.09013

openalex publication_date 2021/08/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

This work is a sequel of a previous work of one of the authors (Y. ^O), which\ntreated certain congruence relation between an elliptic Gauss sum and a\ncoefficient of power series expansion at the origin of the lemniscate sine\nfunction. We extend the previous result (in citeO) which concerned only for\nnon-vanishing elliptic Gauss sums. We give new congruence relations between\npower series coefficients of the lemniscate cosine function, which hold if and\nonly if the corresponding elliptic Gauss sum vanishes.\n

Citations

• Elliptic Gauss Sums and Hecke L-values at s=1
• Good Reduction of Abelian Varieties

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