Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-8

On a sum involving the integral part function

Bo Chen

Received August 7, 2023. Published online February 20, 2024.

Abstract: Let $[t]$ be the integral part of a real number $t$, and let $f$ be the arithmetic function satisfying some simple condition. We establish a new asymptotical formula for the sum $S_f (x)=\sum_{n\le x}f([ x/ n ])$, which improves the recent result of J. Stucky (2022).

Keywords: asymptotical formula; exponential sum; exponential pair; integral part

Classification MSC: 11L07, 11N37

DOI: 10.21136/CMJ.2024.0360-23

PDF available at: Springer Institute of Mathematics CAS

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Affiliations: Bo Chen, Sanda University, 2727 Jinhai Rd, Pudong, Shanghai, 201209, P. R. China, e-mail: bochen@sandau.edu.cn

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