Numerical Computations Concerning the GRH

Abstract

We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus q<=400,000. For even q, we check to height t_0=max(1e8/q,7.5e7/q+200) and for odd q to height t_0=max(1e8/q,3.75e7/q+200).

15 pages

References in corpus (1)

• Minor arcs for Goldbach's problem

Cited by in corpus (2)

• The ternary Goldbach conjecture is true
• Minor arcs for Goldbach's problem