On Arithmetic Series involving the fractional part function
Alexander E. Patkowski
TL;DR
This paper explores new relationships involving the fractional part function, presents a general formula with the Von Mangoldt function, and offers a criterion related to the Riemann Hypothesis.
Contribution
It introduces novel formulas connecting the fractional part function with prime number theory and provides a new criterion for the Riemann Hypothesis.
Findings
New relationships between fractional part function and prime number theory
A general formula involving the Von Mangoldt function
A new criterion for the Riemann Hypothesis
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 a criteria for the Riemann Hypothesis.
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