# Vanishing of Dirichlet L-functions at the central point over function fields

@article{Donepudi2020VanishingOD, title={Vanishing of Dirichlet L-functions at the central point over function fields}, author={Ravi Donepudi and Wanlin Li}, journal={Rocky Mountain Journal of Mathematics}, year={2020} }

We give a geometric criterion for Dirichlet L-functions associated to cyclic characters over the rational function field Fq(t) to vanish at the central point s = 1/2. The idea is based on the observation that vanishing at the central point can be interpreted as the existence of a map from the projective curve associated to the character to some abelian variety over Fq. Using this geometric criterion, we obtain a lower bound on the number of cubic characters over Fq(t) whose L-functions vanish…

## 2 Citations

### On the Vanishing of Twisted L-Functions of Elliptic Curves

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- 2022

The random matrix model of Katz and Sarnak is used to develop a heuristic for the frequency of vanishing of the twisted Lfunctions LE (l, X), as X runs over the Dirichlet characters of order 3.

### Arithmetics, Interrupted

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I share some of my adventures in mathematical research and homeschooling in the time of COVID-19, where my son is studying for his GCSEs and I am a teacher.

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