|
Zapiski Nauchnykh Seminarov POMI, 1994, Volume 211, Pages 104–119
(Mi znsl5881)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
A shortened equation for convolutions
A. I. Vinogradov St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Abstract:
The zeta functions of convolutions are Dirichlet series of the general form $\sum^\infty a_n\cdot n^{-s}$ therefore, they are well convergent in the right half-plane $\operatorname{Re}s>1$. In the critical strip $\operatorname{re}s\in(0,1)$ the convolutions can be represented in terms of the Linnik–Selberg zeta functions whose coefficients are Kloosterman sums. In the present paper, these two representations are combined into a single representation in the same way as the shortened equation for the classical Riemann zeta function. Bibliography: 10 titles.
Received: 14.01.1994
Citation:
A. I. Vinogradov, “A shortened equation for convolutions”, Problems in the theory of representations of algebras and groups. Part 3, Zap. Nauchn. Sem. POMI, 211, Nauka, St. Petersburg, 1994, 104–119; J. Math. Sci., 83:5 (1997), 626–636
Linking options:
https://www.mathnet.ru/eng/znsl5881 https://www.mathnet.ru/eng/znsl/v211/p104
|
Statistics & downloads: |
Abstract page: | 122 | Full-text PDF : | 68 |
|