Hypergeometric L-functions in average polynomial time

Abstract

We describe an algorithm for computing, for all primes $p\le X$, 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.

15 pages, 1 figure; v4 several exposition improvements as suggested the referees