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Zapiski Nauchnykh Seminarov LOMI, 1981, Volume 109, Pages 41–82
(Mi znsl3919)
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This article is cited in 3 scientific papers (total in 3 papers)
Analogues of the Gauss–Vinogradov formula on the critical line
A. I. Vinogradov, L. A. Takhtadzhyan
Abstract:
An asymptotic behavior of the sum $\sum_{p\equiv v(\operatorname{mod}4),\ p\le X}L(s,\chi_p)$ for $X\to\infty$ is studied in the critical strip, where $L(s,\chi_p)$ is the Dirichlet series with the quadratic character $\chi_p$ modulo $p$, where $p$ is a prime number; $v=1$ or $3$. With the help of large seive estimates a formula for this sum is obtained with two asymptotic terms on the critical line of the variable $s$. As a corollary the asymptotic expansion of this sum at the point $s=1/2$ is presented. The asymptotic formula for the sum $\sum_{|d|\le X}L(s,\chi_d)$, where $d$ runs over discriminants of quadratic fields, is also obtained.
Citation:
A. I. Vinogradov, L. A. Takhtadzhyan, “Analogues of the Gauss–Vinogradov formula on the critical line”, Differential geometry, Lie groups and mechanics. Part IV, Zap. Nauchn. Sem. LOMI, 109, "Nauka", Leningrad. Otdel., Leningrad, 1981, 41–82; J. Soviet Math., 24:2 (1984), 183–208
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https://www.mathnet.ru/eng/znsl3919 https://www.mathnet.ru/eng/znsl/v109/p41
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Abstract page: | 266 | Full-text PDF : | 79 |
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