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Chapitre D'ouvrage Année : 2018

On the Missing Log Factor

Résumé

This is a written account of a talk with the same title given during the main Chaire Morlet conference. Its guideline is the elementarily proven bound |\sum _{n\leqslant x}\mu (n)/n|\leqslant 1. The trivial bound for the implied summation is \log x+ \operatorname {\mathrm {\mathcal {O}}}(1), while the Prime Number Theorem tells us that it is o(1). Our starting estimate thus lies in-between, a fact that we explore under different lights.
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Dates et versions

hal-02016308 , version 1 (12-02-2019)

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Olivier Ramare. On the Missing Log Factor. Ferenczi, S; KulagaPrzymus, J; Lemanczyk, M. ERGODIC THEORY AND DYNAMICAL SYSTEMS IN THEIR INTERACTIONS WITH ARITHMETICS AND COMBINATORICS, 2213, SPRINGER INTERNATIONAL PUBLISHING AG, pp.293-315, 2018, Lecture Notes in Mathematics, 978-3-319-74908-2; 978-3-319-74907-5. ⟨10.1007/978-3-319-74908-2_15⟩. ⟨hal-02016308⟩
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