A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture

Masahito Hayashi, Kazuyasu Shigemoto and Takuya Tsukioka
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Masahito Hayashi: Osaka Institute of Technology, Japan
Kazuyasu Shigemoto: Tezukayama University, Japan
Takuya Tsukioka: Bukkyo University, Japan

European Journal of Mathematics and Statistics, 2024, vol. 5, issue 6, 7-15

Abstract: For quadratic curves over finite fileds, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.

Keywords: Analogue of the modular form; analogue of the Taniyama- Shimura conjecture; generalized Gaussian sum (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:5:y:2024:i:6:id:14378

DOI: 10.24018/ejmath.2024.5.6.378

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