2025/11/13 by Daniel R. Johnston, Tim Trudgian, Johnston, Daniel R. +1
#math.NT
paper · pdf · doi:10.48550/arxiv.2511.09978
We explore a method, going back to Landau and developed by Pintz, for connecting sums of arithmetic functions with zero-free regions for L-functions. In particular, we make explicit a general result of Pintz of this form; showing how one can use arithmetical information to deduce information about zeroes of L-functions, rather than the other way around. As a prototype, we work through an example with the Riemann zeta-function and sums of the Möbius function, but we also outline the utility of this method in general.