Partial sums of the Möbius function in arithmetic progressions assuming GRH

2011/11/14 by Karin Halupczok, Halupczok, Karin, Benjamin Suger +1 · 2 citations
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1111.3305

To be published in Functiones et Approximatio

arxiv created 2011/11/14 · arxiv updated 2011/11/15

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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