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arXiv · 1801.02873

Vanishing of Hyperelliptic L-functions at the Central Point

Wanlin Li
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Abstract

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.

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Wanlin Li. 2018-06-27. Vanishing of Hyperelliptic L-functions at the Central Point. https://doi.org/10.1016/j.jnt.2018.03.018

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