Geodesic
On a sum involving the integral part function
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 437-444
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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).
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).
DOI : 10.21136/CMJ.2024.0360-23
Classification : 11L07, 11N37
Keywords: asymptotical formula; exponential sum; exponential pair; integral part 
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Chen, Bo. On a sum involving the integral part function. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 437-444. doi: 10.21136/CMJ.2024.0360-23

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