Sums with the Möbius function twisted by characters with powerful moduli

Banks, William; Shparlinski, Igor

doi:10.1090/tran/7914

Sums with the Möbius function twisted by characters with powerful moduli
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by William D. Banks and Igor E. Shparlinski PDF

Trans. Amer. Math. Soc. 373 (2020), 249-272 Request permission

Abstract:

In a 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 with the Möbius function twisted by characters of the same type, which complements and improves some earlier work of B. Green (2012). To achieve this, we obtain a series of results about the size and zero-free region of $L$-functions with the same class of moduli.

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