Cite this article as:

Kuznetsov V. N., Polyakova O. A. On Characterization Determining Entire Functions and Consistent with Riman’s Type Equation Dirichlet’s Series with Finetly-Valued Coefficients. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2011, vol. 11, iss. 3, pp. 21-25. DOI: https://doi.org/10.18500/1816-9791-2011-11-3-1-21-25

Language: 
Russian
Heading: 
Mathematics
UDC: 
511.3

On Characterization Determining Entire Functions and Consistent with Riman’s Type Equation Dirichlet’s Series with Finetly-Valued Coefficients

Authors: 
Kuznetsov Valentin Nikolaevich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , KuznetsovVN@info.sgu.ru
Polyakova O. A., Saratov State University, Russia, Saratov, Astrakhanskaya 83 , KuznetsovVN@info.sgu.ru
Abstract: 

In the investigation were founded specifications for Dirichlet’s series coefficients, wherein this series determine entire function and measure up functional Riman’s type equation. Were shown that exist infinit multitude of such series that are different from Dirichlet’s L-functions.

Key words: 
Dirichlet’s series, functional equation, Dirichlet’s L-function.
DOI: 
https://doi.org/10.18500/1816-9791-2011-11-3-1-21-25
References

1. Карацуба А. А. Основы аналитической теории чисел. М.: Наука, 1975.
2. Воронин С. М., Карацуба А. А. Дзета-функция Римана. М.: Физматгиз, 1994.
3. Прахар К. Распределение простых чисел. М.: Мир, 1967.

4. Кузнецов В. Н. Аналог теоремы Сеге для одного класса рядов Дирихле // Мат. заметки. 1984. Т. 36, вып. 9. С. 805–813.
5. Чандрасекхаран К. Арифметические функции. М.: Наука, 1975.

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