The prime number race and zeros of Dirichlet $L$-functions off the critical line. III

Abstract

We show, for any $q\ge 3$ and distinct reduced residues $a,b(\mathrm{mod}q)$, the existence of certain hypothetical sets of zeros of Dirichlet $L$-functions lying off the critical line implies that $\pi (x;q,a)<\pi (x;q,b)$ for a set of real $x$ of asymptotic density 1.

8 pages

References in corpus (1)

• On the multiplicity of zeros of the zeta-function