Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896826 | Journal of Number Theory | 2018 | 19 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Wanlin Li,