Article
| Title: | Averaging some multiplicative functions under the hereditary sum of digits (English) |
| Author: | Aloui, Karam |
| Author: | Maatoug, Mabrouk |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 66 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 1-28 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | The aim of this paper is to conduct a survey on the average of some selected multiplicative arithmetic functions for large values of integers, while considering constraints imposed by the hereditary sum of digits function in base $b$, denoted by $w_{b}$. This investigation aims to provide insights into the behavior of these functions within the scope of the hereditary sum of digits. (English) |
| Keyword: | exponential sum |
| Keyword: | multiplicative arithmetic function |
| Keyword: | hereditary sum of digits function |
| MSC: | 11A07 |
| MSC: | 11A25 |
| MSC: | 11A67 |
| MSC: | 11L07 |
| MSC: | 11N37 |
| MSC: | 11N60 |
| MSC: | 11N69 |
| DOI: | 10.14712/1213-7243.2026.008 |
| . | |
| Date available: | 2026-05-15T05:53:00Z |
| Last updated: | 2026-05-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153609 |
| . | |
| Reference: | [1] Aloui K.: On the order of magnitude of some arithmetical functions under digital constraint I.Proc. Indian Acad. Sci. Math. Sci. 125 (2015), no. 4, 457–476. 10.1007/s12044-015-0231-x |
| Reference: | [2] Aloui K.: On the average of some arithmetical functions under a constraint on the sum of digits of squares.Hiroshima Math. J. 46 (2016), no. 1, 37–54. 10.32917/hmj/1459525929 |
| Reference: | [3] Aloui K.: On the order of magnitude of some arithmetical functions under digital constraint II.Math. Rep. (Bucur.) 24 (74) (2022), no. 3, 403–423. |
| Reference: | [4] Aloui K., Feki F.: On the distribution of the integers with missing digits under hereditary sum of digits.Publ. Math. Debrecen 94 (2019), no. 3–4, 337–358. 10.5486/PMD.2019.8295 |
| Reference: | [5] Amri M., Mbarki K.: Mean values of arithmetic functions under congruences with the Euler function.Turkish Journal of Analysis and Number Theory 8 (2020), no. 2, 39–48. 10.12691/tjant-8-2-4 |
| Reference: | [6] Andrica D., Piticari M.: On some extensions of Jordan's arithmetic functions.Acta Univ. Apulensis Math. Inform. 7 (2004), 13–22. |
| Reference: | [7] Apostol T. M.: Introduction to Analytic Number Theory.Undergraduate Texts in Mathematics, Springer, New York, 1976. |
| Reference: | [8] Balakrishnan U., Pétermann Y.-F. S.: Asymptotic estimates for a class of summatory functions. II.Comment. Math. Univ. St. Pauli 50 (2001), no. 1, 89–109. |
| Reference: | [9] Bésineau J.: Indépendance statistique d'ensembles liés à la fonction “somme des chiffres".Acta Arith. 20 (1972), 401–416 (French). 10.4064/aa-20-4-401-416 |
| Reference: | [10] Coquet J.: Sur les fonctions $Q$-multiplicatives et $Q$-additives.Thèse 3 cycle, Orsay, 1975 (French). |
| Reference: | [11] Delange H.: Sur les fonctions $q$-additives ou $q$-multiplicatives.Acta Arith. 21 (1972), no. 1, 285–298. 10.4064/aa-21-1-285-298 |
| Reference: | [12] Drmota M., Mauduit C., Rivat J.: Primes with an average sum of digits.Compos. Math. 145 (2009), no. 2, 271–292. 10.1112/S0010437X08003898 |
| Reference: | [13] Feki F.: On the hereditary sum of digits function to base $q$.J. Ramanujan Math. Soc. 36 (2021), no. 2, 157–168. |
| Reference: | [14] Goodstein R. L.: On the restricted ordinal theorem.J. Symbolic Logic 9 (1944), no. 2, 33–41. 10.2307/2268019 |
| Reference: | [15] Halberstam H., Richert H.-E.: Mean value theorems for a class of arithmetic functions.Acta Arith. 18 (1971), no. 1, 243–256. 10.4064/aa-18-1-243-256 |
| Reference: | [16] Hardy G. H., Wright E. M.: An Introduction to the Theory of Numbers.The Clarendon Press, Oxford University Press, New York, 1979. |
| Reference: | [17] Ikehara S.: An extension of Landau's theorem in the analytical theory of numbers.J. of Math. Phys. 10 (1931), no. 1–4, 1–12. 10.1002/sapm19311011 |
| Reference: | [18] Jemai A.: On the average of some multiplicative functions under a constraint on joint Zeckendorf representation.Hiroshima Math. J. 55 (2025), no. 1, 1–21. 10.32917/h2023005 |
| Reference: | [19] Kátai I.: Distribution of $q$-additive functions.in Probability Theory and Applications, Math. Appl., 80, Kluwer Acad. Publ., Dordrecht, 1992, pages 309–318. |
| Reference: | [20] Kirby L., Paris J.: Accessible independence results for Peano arithmetic.Bull. Lond. Math. Soc. 14 (1982), no. 4, 285–293. 10.1112/blms/14.4.285 |
| Reference: | [21] Lehmer D. H.: Euler constants for arithmetical progressions.Acta Arith. 27 (1975), 125–142. 10.4064/aa-27-1-125-142 |
| Reference: | [22] Levin B. V., Faĭnleĭb A. S.: Application of certain integral equations to questions of the theory of numbers.Uspehi Mat. Nauk 22 (1967), no. 3(135), 119–197 (Russian). |
| Reference: | [23] van Lint J. H., Richert H.-E.: On primes in arithmetic progressions.Acta Arith. 11 (1965), 209–216. 10.4064/aa-11-2-209-216 |
| Reference: | [24] Mbarki K., Wannes W.: Means of some arithmetical functions on shifted smooth numbers in arithmetic progression.Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 4, Paper No. 53, 22 pages. 10.1007/s12044-019-0521-9 |
| Reference: | [25] Sanna C.: On the exponential sum with the sum of digits of hereditary base $b$ notation.Integers 14 (2014), Paper No. A36, 10 pages. |
| Reference: | [26] Tóth L.: A Survey of gcd-sum functions.J. Integer Seq. 13 (2010), no. 8, Article 10.8.1, 23 pages. |
| Reference: | [27] Wiener N.: A note on Tauberian theorems.Ann. of Math. (2) 33 (1932), no. 4, 787. 10.2307/1968223 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
