Vanishing of hyperelliptic L-functions at the central point

JOURNAL OF NUMBER THEORY

卷:191

Article

Li, Wanlin¹ 

[1] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 USA

关键词: Zeta function;    Hyperelliptic curve;    Elliptic curve;    Finite field;    Function field;   

DOI  :  10.1016/j.jnt.2018.03.018

来源: Elsevier

【 摘 要 】

We obtain a lower bound on the number of quadratic Dirichlet L-functions over the rational function field which vanish at the central point s = 1/2. This is in contrast with the situation over the rational numbers, where a conjecture of Chowla predicts there should be no such L-functions. The approach is based on the observation that vanishing at the central point can be interpreted geometrically, as the existence of a map to a fixed abelian variety from the hyperelliptic curve associated to the character. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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