Hypergeometric L-functions in average polynomial time

Edgar Costa; Kiran S. Kedlaya; David Roe

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arXiv · 2005.13640

Hypergeometric L-functions in average polynomial time

Edgar Costa·Kiran S. Kedlaya·David Roe

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Abstract

We describe an algorithm for computing, for all primes $p \leq X$, the mod-$p$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive in time quasilinear in $X$. This combines the Beukers--Cohen--Mellit trace formula with average polynomial time techniques of Harvey et al.

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Edgar Costa, Kiran S. Kedlaya, David Roe. 2020-05-27. Hypergeometric L-functions in average polynomial time. https://arxiv.org/abs/2005.13640

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