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A note on the 2 k-th mean value of the Hurwitz zeta function

Published online by Cambridge University Press:  17 April 2009

A. Kumchev
A. Kumchev
Affiliation:
Department of MathematicsUniversity of South CarolinaColumbia SC 29208United States of America e-mail: koumtche@math.sc.edu
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Consider the error term in the asymptotic formula

In this note we obtain δ(k) ≍ 1/(k6 log2k) which, for large values of k, presents a substantial improvement over the previously known result .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 403 - 405
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Arkhipov, G.I., Chubarikov, V.N. and Karatsuba, A.A., Theory of multiple exponential sums, (in Russian) (Nauka, Moscow, 1987).Google Scholar
[2]Karatsuba, A.A. and Voronin, S.M., The Riemann zeta function (Walter de Gruyter & Co., Berlin, 1992).CrossRefGoogle Scholar
[3]Wang, Y., ‘On the 2k-th mean value of Hurwitz zeta function’, Acta Math. Hungar. 74 (1997), 301–307.Google Scholar