Email this article On the universality of the zeta functions of certain cusp forms
- Authors: Laurinčikas A.1
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Affiliations:
- Faculty of Mathematics and Informatics, Vilnius University
- Issue: Vol 213, No 5 (2022)
- Pages: 88-100
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133448
- DOI: https://doi.org/10.4213/sm9650
- ID: 133448
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Abstract
We consider a certain Dirichlet series associated with the zeta function of a normalized Hecke cusp form. It is absolutely convergent on the right of the critical strip. We obtain universality theorems on the approximation of a wide class of analytic functions by shifts of this series. Bibliography: 9 titles.
About the authors
Antanas Laurinčikas
Faculty of Mathematics and Informatics, Vilnius University
Email: antanas.laurincikas@mif.vu.lt
Doctor of physico-mathematical sciences, Professor
References
- С. М. Воронин, “Теорема об “универсальности” дзета-функции Римана”, Изв. АН СССР. Сер. матем., 39:3 (1975), 475–486
- A. Laurinčikas, K. Matsumoto, “The universality of zeta-functions attached to certain cusp forms”, Acta Arith., 98:4 (2001), 345–359
- A. Laurinčikas, K. Matsumoto, J. Steuding, “Discrete universality of $L$-functions of new forms. II”, Lith. Math. J., 56:2 (2016), 207–218
- B. Bagchi, The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, PhD thesis, Indian Stat. Inst., Calcutta, 1981, viii+172 pp.
- А. Каченас, А. Лауринчикас, “О рядах Дирихле, связанных с некоторыми параболическими формами”, Liet. Mat. Rink., 38:1 (1998), 113–124
- Г. Монтгомери, Мультипликативная теория чисел, Мир, М., 1974, 160 с.
- M. Jutila, “On the approximate functional equation for $zeta^2(s)$ and other Dirichlet series”, Quart. J. Math. Oxford Ser. (2), 37:2 (1986), 193–209
- П. Биллингсли, Сходимость вероятностных мер, Наука, М., 1977, 351 с.
- С. Н. Мергелян, “Равномерные приближения функций комплексного переменного”, УМН, 7:2(48) (1952), 31–122
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