电邮这篇文章 Universality of $L$-Dirichlet functions and nontrivial zeros of the Riemann zeta-function
- 作者: Laurinčikas A.P.1, Petuškinaitė J.1
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隶属关系:
- Faculty of Mathematics and Informatics, Vilnius University
- 期: 卷 210, 编号 12 (2019)
- 页面: 98-119
- 栏目: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133304
- DOI: https://doi.org/10.4213/sm9194
- ID: 133304
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详细
We prove a joint discrete universality theorem for Dirichlet $L$-functions concerning joint approximation of a tuple of analytic functions by shifts $L(s+ih\gamma_k, \chi_1),…,L(s+ih\gamma_k,\chi_r)$, where $0<\gamma_1<\gamma_2<\dotsb$ is the sequence of imaginary parts of the nontrivial zeros of the Riemann zeta-function, $h$ is a fixed positive number, and $\chi_1,…,\chi_r$ are pairwise nonequivalent Dirichlet characters. We use a weak form of Montgomery's conjecture on the correlation of pairs of zeros of the Riemann zeta-function in the analysis. Moreover, we show the universality of certain compositions of Dirichlet $L$-functions with operators in the space of analytic functions. Bibliography: 31 titles.
作者简介
Antanas Laurinčikas
Faculty of Mathematics and Informatics, Vilnius University
Email: antanas.laurincikas@mif.vu.lt
Doctor of physico-mathematical sciences, Professor
Jurgita Petuškinaitė
Faculty of Mathematics and Informatics, Vilnius University
参考
- 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
- P. Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York–London–Sydney, 1968, xii+253 pp.
- E. Buivydas, A. Laurinčikas, “A discrete version of the Mishou theorem”, Ramanujan J., 38:2 (2015), 331–347
- E. Buivydas, A. Laurinčikas, “A generalized discrete universality theorem for the Riemann and Hurwitz zeta-functions”, Lith. Math. J., 55:2 (2015), 193–206
- R. Garunkštis, A. Laurinčikas, R. Macaitien{. e}, “Zeros of the Riemann zeta-function and its universality”, Acta Arith., 181:2 (2017), 127–142
- A. Dubickas, A. Laurinčikas, “Joint discrete universality of Dirichlet $L$-functions”, Arch. Math. (Basel), 104:1 (2015), 25–35
- A. Dubickas, A. Laurinčikas, “Distribution modulo 1 and the discrete universality of the Riemann zeta-function”, Abh. Math. Semin. Univ. Hambg., 86:1 (2016), 79–87
- Х. Хейер, Вероятностные меры на локально компактных группах, Мир, М., 1981, 702 с.
- Л. Кейперс, Г. Нидеррейтер, Равномерное распределение последовательностей, Наука, М., 1985, 408 с.
- A. Laurinčikas, Limit theorems for the Riemann zeta-function, Math. Appl., 352, Kluwer Acad. Publ., Dordrecht, 1996, xiv+297 pp.
- A. Laurinčikas, “On joint universality of Dirichlet $L$-functions”, Чебышевский сб., 12:1 (2011), 124–139
- A. Laurinčikas, “Discrete universality of the Riemann zeta-function and uniform distribution modulo 1”, Алгебра и анализ, 30:1 (2018), 139–150
- А. Лауринчикас, “Совместная дискретная универсальность дзета-функций Гурвица”, Матем. сб., 205:11 (2014), 75–94
- А. Лауринчикас, “Дискретная версия теоремы Мишу. II”, Аналитическая и комбинаторная теория чисел, Сборник статей. К 125-летию со дня рождения академика Ивана Матвеевича Виноградова, Тр. МИАН, 296, МАИК «Наука/Интерпериодика», М., 2017, 181–191
- A. Laurinčikas, “Joint value distribution theorems for the Riemann and Hurwitz zeta-functions”, Mosc. Math. J., 18:2 (2018), 349–366
- A. Laurinčikas, “Joint discrete universality for periodic zeta-functions”, Quaest. Math., 42:5 (2019), 687–699
- A. Laurinčikas, R. Macaitien{. e}, D. Šiaučiūnas, “Uniform distribution modulo 1 and the joint universality of Dirichlet $L$-functions”, Lith. Math. J., 56:4 (2016), 529–539
- А. Лауринчикас, Л. Мешка, “Уточнение неравенства универсальности”, Матем. заметки, 96:6 (2014), 905–910
- R. Macaitien{. e}, “On discrete universality of the Riemann zeta-function with respect to uniformly distributed shifts”, Arch. Math. (Basel), 108:3 (2017), 271–281
- С. Н. Мергелян, “Равномерные приближения функций комплексного переменного”, УМН, 7:2(48) (1952), 31–122
- H. L. Montgomery, “The pair correlation of zeros of the zeta function”, Analytic number theory (St. Louis Univ., St. Louis, MO, 1972), Proc. Sympos. Pure Math., 24, Amer. Math. Soc., Providence, RI, 1973, 181–193
- Г. Монтгомери, Мультипликативная теория чисел, Мир, М., 1974, 160 с.
- Ł. Pankowski, “Joint universality for dependent $L$-functions”, Ramanujan J., 45:1 (2018), 181–195
- A. Reich, “Werteverteilung von Zetafunktionen”, Arch. Math. (Basel), 34 (1980), 440–451
- J. Steuding, Value-distribution of $L$-functions, Lecture Notes in Math., 1877, Springer, Berlin, 2007, xiv+317 pp.
- J. Steuding, “The roots of the equation $zeta(s)=a$ are uniformly distributed modulo one”, Analytic and probabilistic methods in number theory, TEV, Vilnius, 2012, 243–249
- E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., The Clarendon Press, Oxford Univ. Press, New York, 1986, x+412 pp.
- С. М. Воронин, “Теорема об “универсальности” дзета-функции Римана”, Изв. АН СССР. Сер. матем., 39:3 (1975), 475–486
- С. М. Воронин, “О функциональной независимости $L$-функций Дирихле”, Acta Arith., 27 (1975), 493–503
- С. М. Воронин, А. А. Карацуба, Дзета-функция Римана, Физматлит, М., 1994, 376 с.
- С. М. Воронин, Избранные труды: математика, Изд-во МГТУ им. Н. Э. Баумана, М., 2006, 480 с.
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