On an analogue of Gelfond's problem for Ostrowsky expansion
- Autores: Zhukova A.A.1, Shutov A.V.2
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Afiliações:
- Russian Academy of National Economy and Public Administration under the President of the Russian Federation (Vladimir Branch)
- Vladimir State University
- Edição: Volume 89, Nº 2 (2025)
- Páginas: 25-44
- Seção: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/303945
- DOI: https://doi.org/10.4213/im9633
- ID: 303945
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Resumo
The paper considers an analogue of A. O. Gelfond's problem on the distribution of sums of digits of $b$-ary expansions of natural numbers in arithmetic progressions. Instead of $b$-ary expansions,we consider expansions in the Ostrowsky numeration system associated with arbitrary irrational $\alpha$.
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Sobre autores
Alla Zhukova
Russian Academy of National Economy and Public Administration under the President of the Russian Federation (Vladimir Branch)
Autor responsável pela correspondência
Email: georg967@mail.ru
Candidate of physico-mathematical sciences, Associate professor
Anton Shutov
Vladimir State University
Email: a1981@mail.ru
Doctor of physico-mathematical sciences, Associate professor
Bibliografia
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- M. Lamberger, J. W. Thuswaldner, “Distribution properties of digital expansions arising from linear recurrences”, Math. Slovaca, 53:1 (2003), 1–20
- A. Ostrowsky, “Bemerkungen zur Theorie der Diophantischen Approximationen”, Abh. Math. Semin. Univ. Hambg., 1:1 (1922), 77–98
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- D. Sharma, “Joint distribution in residue classes of the base-$q$ and Ostrowski digital sums”, Unif. Distrib. Theory, 14:2 (2019), 1–26
- А. А. Жукова, А. В. Шутов, “Об аналоге задачи Гельфонда для обобщенных разложений Цеккендорфа”, Чебышевский сб., 22:2 (2021), 104–120
- T. Stoll, “Combinatorial constructions for the Zeckendorf sum of digits of polynomial values”, Ramanujan J., 32:2 (2013), 227–243
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