Vol. 4, No. 1, 2020

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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 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
Milestones
Received: 28 February 2020
Revised: 4 August 2020
Accepted: 24 August 2020
Published: 29 December 2020
Authors
Edgar Costa
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Kiran S. Kedlaya
Department of Mathematics
University of California, San Diego
La Jolla, CA
United States
David Roe
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States