Article
| Title: | On a sum involving the integral part function (English) |
| Author: | Chen, Bo |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 437-444 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | 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). (English) |
| Keyword: | asymptotical formula |
| Keyword: | exponential sum |
| Keyword: | exponential pair |
| Keyword: | integral part |
| MSC: | 11L07 |
| MSC: | 11N37 |
| idZBL: | Zbl 07893392 |
| idMR: | MR4764533 |
| DOI: | 10.21136/CMJ.2024.0360-23 |
| . | |
| Date available: | 2024-07-10T14:52:27Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152451 |
| . | |
| Reference: | [1] Apostol, T. M.: Introduction to Analytic Number Theory.Undergraduate Texts in Mathematics. Springer, New York (1976). Zbl 0335.10001, MR 0434929, 10.1007/978-1-4757-5579-4 |
| Reference: | [2] Bordellès, O.: Arithmetic Tales.Universitext. Springer, London (2012). Zbl 1244.11001, MR 2952910, 10.1007/978-1-4471-4096-2 |
| Reference: | [3] Bordellès, O., Dai, L., Heyman, R., Pan, H., Shparlinski, I. E.: On a sum involving the Euler function.J. Number Theory 202 (2019), 278-297. Zbl 1454.11009, MR 3958074, 10.1016/j.jnt.2019.01.006 |
| Reference: | [4] Graham, S. W., Kolesnik, G.: Van der Corput's Method for Exponential Sums.London Mathematical Society Lecture Note Series 126. Cambridge University Press, Cambridge (1991). Zbl 0713.11001, MR 1145488, 10.1017/CBO9780511661976 |
| Reference: | [5] Liu, K., Wu, J., Yang, Z.: A variant of the prime number theorem.Indag. Math., New Ser. 33 (2022), 388-396. Zbl 1487.11087, MR 4383117, 10.1016/j.indag.2021.09.005 |
| Reference: | [6] Ma, J., Sun, H.: On a sum involving the divisor function.Period. Math. Hung. 83 (2021), 185-191. Zbl 1499.11293, MR 4344126, 10.1007/s10998-020-00378-3 |
| Reference: | [7] Ma, J., Wu, J.: On a sum involving the Mangoldt function.Period. Math. Hung. 83 (2021), 39-48. Zbl 1488.11151, MR 4260147, 10.1007/s10998-020-00359-6 |
| Reference: | [8] Mercier, A., Nowak, W. G.: On the asymptotic behaviour of sums $\sum g\left(n\right)\{x/n\}^k$.Monatsh. Math. 99 (1985), 213-221. Zbl 0555.10027, MR 0791682, 10.1007/BF01295155 |
| Reference: | [9] Stucky, J.: The fractional sum of small arithmetic functions.J. Number Theory 238 (2022), 731-739. Zbl 1508.11082, MR 4430115, 10.1016/j.jnt.2021.09.015 |
| Reference: | [10] Wu, J.: Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski.Period. Math. Hung. 80 (2020), 95-102. Zbl 1449.11011, MR 4059866, 10.1007/s10998-019-00300-6 |
| Reference: | [11] Zhai, W.: On a sum involving the Euler function.J. Number Theory 211 (2020), 199-219. Zbl 1437.11119, MR 4074554, 10.1016/j.jnt.2019.10.003 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
