Affiliation:
1. Institute of Analysis and Number Theory Graz University of Technology Graz Austria
Abstract
AbstractIt is proved that as , uniformly for all positive integers , we have
where . Here, is the Dickman function. We have and when , which significantly improves previous results in [17, 40]. Similar results are established for Dirichlet L‐functions. On the other hand, when assuming the Riemann hypothesis and the generalized Riemann hypothesis, we establish upper bounds for and . Furthermore, when assuming the Granville–Soundararajan conjecture is true, we establish the following asymptotic formulas:
where is prime and is given.