# Local Statistics for Zeros of Artin-Schreier L-functions

@inproceedings{Entin2021LocalSF, title={Local Statistics for Zeros of Artin-Schreier L-functions}, author={Alexei Entin and Noam Pirani}, year={2021} }

We study the local statistics of zeros of L-functions attached to Artin-Scheier curves over finite fields. We consider three families of Artin-Schreier L-functions: the ordinary, polynomial (the p-rank 0 stratum) and odd-polynomial families. We compute the 1-level zero-density of the first and third families and the 2-level density of the second family for test functions with Fourier transform supported in a suitable interval. In each case we obtain agreement with a unitary or symplectic random…

## One Citation

Moments of Traces of Frobenius of Higher Order Dirichlet $L$-functions over $\mathbb{F}_q[T]$

- Mathematics
- 2021

We study the moments of Tr(Θχ) as χ runs over Dirichlet characters defined over Fq [T ] of fixed order r. In particular, we show that after an appropriate normalization, the q-limit of the power sum…

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