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Note on the mean absolute value theorem for the Dirichlet's $L$-function in the critical stripe
L. G. Arkhipova, V. N. Chubarikov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics (Moscow)
Abstract:
In the paper we are continued investigations on a generalization and a improvement of the R. T. Turganaliev's result by the deduction of the asymptotic formula for the mean-value of the Rieman's zeta-function in the critical stripe with the rest term, having the power in the reduction. We are found the asymptotics of Dirichlet's $L$-function in the critical stripe, which improves the R. T. Turganaliev's theorem on the zeta-function for all values of the real part ($1/2<\mathrm{Re}\, s\leq 1$). This result are got for the account of the different using of estimations of trigonometric sums on the base of the second derivative in the exponent.
Keywords:
Dirichlet's characters, Dirichlet's functions, the zeta-sum twisted together with the Dirichlet's character.
Received: 03.12.2020 Accepted: 21.02.2021
Citation:
L. G. Arkhipova, V. N. Chubarikov, “Note on the mean absolute value theorem for the Dirichlet's $L$-function in the critical stripe”, Chebyshevskii Sb., 22:1 (2021), 67–75
Linking options:
https://www.mathnet.ru/eng/cheb987 https://www.mathnet.ru/eng/cheb/v22/i1/p67
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Abstract page: | 125 | Full-text PDF : | 47 | References: | 24 |
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