Hypergeometric L-functions in average polynomial time
Edgar Costa, Kiran S. Kedlaya, David Roe · The Open Book Series · 2020
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. Costa and Roe were supported by the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation via Simons Foundation grant 550033. Kedlaya