Partial sums of the Möbius function in arithmetic progressions assuming GRH

Partial sums of the Möbius function in arithmetic progressions assuming GRH

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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Veröffentlicht in:arXiv.org 2011-11
Hauptverfasser: Halupczok, Karin, Suger, Benjamin
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
Number theory
Progressions
Upper bounds
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Zusammenfassung: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.
ISSN:2331-8422