A triple Mertens evaluation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Popa, Dumitru¹ 

[1] Ovidius Univ Gonstanta, Dept Math, Bd Mamaia 124, Constanta 900527, Romania

关键词: Arithmetic functions;    Asymptotic results;    Mertens type evaluations;    Dilogarithm;    Trilogarithm;   

DOI  :  10.1016/j.jmaa.2016.06.054

来源: Elsevier

【 摘 要 】

We prove the following triple Mertens evaluation Sigma(pqr <= x, p,q,r prime) 1/pqr = (ln (ln x) B)(3) - pi(2)/2 (ln (lnx) + B) + 2 zeta (3) + O (ln(2) (lnx)/lnx) where B is the Mertens constant and zeta is the Rieman zeta function. (C) Elsevier Inc. All rights reserved.

【 授权许可】

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