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  • 1 Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
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Abstract

For the Riemann zeta-function we present an asymptotic formula of a shifted fourth moment in an unbounded shift range along the critical line.

  • [1] Bettin, S. 2010 The second moment of the Riemann zeta-function with unbounded shifts Int. J. Number Theory 6 19331944 .

  • [2] Heath-Brown, D. R. 1979 The fourth power moment of the Riemann zeta function Proc. Lond. Math. Soc. 38 3 385422 .

  • [3] Hughes, C. P. Young, M. P. 2010 The twisted fourth moment of the Riemann zeta function J. Reine Angew. Math. 641 203236 .

  • [4] Ingham, A. E. 1928 Mean-value theorems in the theory of the Riemann zeta-function Proc. Lond. Math. Soc. 27 273300 .

  • [5] Ivić, A. 1985 The Riemann Zeta-function Wiley New York.

  • [6] Montgomery, H. L. Vaughan, R. C. 1974 Hilbert's inequality J. Lond. Math. Soc. 8 7382 .

  • [7] Motohashi, Y. 1997 Spectral Theory of the Riemann Zeta-function Cambridge Tracts Math. 127 Cambridge University Press Cambridge .

  • [8] Ramachandra, K. 1974 A simple proof of the mean fourth power estimate for and Ann. Scuola Norm. Sup. Pisa 1 8197.

  • [9] Ramachandra, K. 1975 Application of a theorem of Montgomery and Vaughan to the zeta-function J. Lond. Math. Soc. 10 482486 .

  • [10] Ramachandra, K. Sankaranarayanan, A. 2003 On an asymptotic formula of Srinivasa Ramanujan Acta Arith. 109 349357 .

  • [11] Titchmarsh, E. C. 1986 The Theory of the Riemann Zeta-function 2 The Clarendon Press, Oxford University Press New York.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)