Root numbers for the Jacobian varieties of Fermat curves

JOURNAL OF NUMBER THEORY

卷:226

Article

Shu, Jie¹ 

[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: Fermat curves;    Root numbers;    L-functions;   

DOI  :  10.1016/j.jnt.2021.03.012

来源: Elsevier

【 摘 要 】

Let p be an odd prime number. Let K be the p-th cyclotomic field. We give general formulae for the root numbers of the Jacobian varieties of the Fermat curves X-p + Y-p = delta where delta is an integer. As an application of these general formulae, we derive the equidistribution of the root numbers for the families of Jacobian varieties of the Fermat curves. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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