The remark on the mean value theorem for the absolute value of Dirichlet L-function in the critical strip
https://doi.org/10.22405/2226-8383-2021-22-1-67-75
Abstract
We continue our researches concerning the generalization and improvement of R.T.Turganaliev’s result that states an asymptotic formula for the mean value of the Riemann zeta function in the critical strip with power factor saving in the remainder term.We find an asymptotic for the mean value of Dirichlet L-function in the critical strip. This assertion improves R.T.Turganaliev’s theorem for zeta-function in the whole interval $$(1/2 < Re 𝑠 ≤ 1)$$. Our result is based on the special use of the estimation of exponential sums by second derivative test.
About the Authors
Lyudmila Gennad’evna Arkhipova
M. V. Lomonosov Moscow State University
Russian Federation
Russian Federation
сandidate of physical and mathematical sciences
Vladimir Nikolaevich Chubarikov
M. V. Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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Review
For citations:
Arkhipova L.G., Chubarikov V.N. The remark on the mean value theorem for the absolute value of Dirichlet L-function in the critical strip. Chebyshevskii Sbornik. 2021;22(1):67-75. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-67-75
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