Jacobi Sums and Hecke Grössencharacters

Abstract

We give an extended abstract regarding our talk, and the associated Magma implementation of Jacobi sums and Hecke Grössencharacters. This builds upon seminal work of Weil (Trans Am Math Soc 73:487–495, 1952), and makes his construction explicitly computable, inherently relying on his upper bound for the conductor. Moreover, we can go slightly further than Weil by additionally allowing Kummer twists of the Jacobi sums. We also note the correspondence of these (twisted) Jacobi sums to tame prime information for hypergeometric motives.

Although our viewpoint and notation is derived from later work of Anderson, we do not use his formalism in any substantial way, and indeed the main thrust of all we do is already in Weil’s work.