On arithmetic series involving the fractional part function

Alexander E. Patkowski

doi:10.21099/tkbjm/20224601145

Abstract

We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the von Mangoldt function is presented, as well as expressions under the Riemann Hypothesis.

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Alexander E. Patkowski. "On arithmetic series involving the fractional part function." Tsukuba J. Math. 46 (1) 145 - 152, July 2022. https://doi.org/10.21099/tkbjm/20224601145

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Received: 5 July 2021; Revised: 10 February 2022; Published: July 2022

First available in Project Euclid: 19 September 2022

MathSciNet: MR4489190

zbMATH: 1497.11192

Digital Object Identifier: 10.21099/tkbjm/20224601145

Subjects:

Primary: 11L20 , 11M06

Keywords: primes , Riemann zeta function , von Mangoldt function

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