#### Vol. 4, No. 1, 2020

 Recent Volumes 5: Gauge Theory and Low-Dimensional Topology 4: ANTS XIV 3: Hillman: Poincaré Duality 2: ANTS XIII 1: ANTS X
 The Open Book Series All Volumes About the Series Ethics Statement Purchase Printed Copies Author Index ISSN (electronic): 2329-907X ISSN (print): 2329-9061 MSP Books and Monographs Other MSP Publications
Hypergeometric $L$-functions in average polynomial time

### Edgar Costa, Kiran S. Kedlaya and David Roe

Vol. 4 (2020), No. 1, 143–159
##### 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.

##### Keywords
hypergeometric L-functions, average polynomial time
##### Mathematical Subject Classification 2010
Primary: 11Y16, 33C20
Secondary: 11G09, 11M38, 11T24