Sums with the Mobius function twisted by characters with powerful moduli
Number Theory
2018-02-01 v1
Abstract
In their recent work, the authors (2016) have combined classical ideas of A. G. Postnikov (1956) and N. M. Korobov (1974) to derive improved bounds on short character sums for certain nonprincipal characters with powerful moduli. In the present paper, these results are used to bound sums of the Mobius function twisted by characters of the same type, complementing and improving some earlier work of B. Green (2012). To achieve this, we obtain a series of results about the size and zero-free region of -functions with the same class of moduli.
Keywords
Cite
@article{arxiv.1801.10276,
title = {Sums with the Mobius function twisted by characters with powerful moduli},
author = {William D. Banks and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1801.10276},
year = {2018}
}