Riemann Hypothesis for L-functions of genus 2 curves over Q

Prove the Riemann hypothesis for the Hasse–Weil L-function L(C,s) associated to the Jacobian of a genus 2 curve over Q, showing that all nontrivial zeros lie on the critical line after analytic continuation.

Background

The authors present an algorithm to efficiently compute local L-polynomials L_p(T) and thereby assemble L(C,s), which is relevant to global analytic questions such as the Riemann hypothesis. They explicitly list the Riemann hypothesis among the open conjectures pertaining to L(C,s).

High-precision and large-range computations of L_p(T) enabled by their lifting method contribute data that can be used to test aspects of the analytic behavior of L(C,s) for genus 2 curves.