Partial sums of the Möbius function in arithmetic progressions assuming GRH

Published 14 Nov 2011 in math.NT | (1111.3305v1)

Abstract: We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K. Soundararajan is extended to L-series.

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