Riemann hypothesis for genus 2 curve L-functions

Prove the Riemann hypothesis for the L-function L(C,s) associated to a genus 2 curve C over Q, establishing that its nontrivial zeros lie on the critical line.

Background

The Riemann hypothesis (in its generalized form for automorphic and motivic L-functions) is one of the central open problems in number theory. For L-functions arising from genus 2 curves, it predicts the location of zeros.

The paper emphasizes that L(C,s) sits among several open conjectures, including the Riemann hypothesis, and presents algorithms that enable efficient computation of local L-factors L_p(T), which supports empirical investigation of such analytic properties.