Abstract
This is Part II of our examination of the second and fourth moments and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations.
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References
E.B. Bogomolny, J.P. Keating, Random matrix theory and the Riemann zeros I: three- and four-point correlations. Nonlinearity 8(6), 1115–1131 (1995)
B. Conrey, J.P. Keating, Moments of zeta and correlations of divisor-sums: I. Philos. Trans. A 373(2040), 20140313, 11 pp (2015)
D.A. Goldston, S.M. Gonek, Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series. Acta Arith. 84(2), 155–192 (1998)
Acknowledgements
We gratefully acknowledge support under EPSRC Programme Grant EP/K034383/1 LMF: L-Functions and Modular Forms. Research of the first author was also supported by the American Institute of Mathematics and by a grant from the National Science Foundation. JPK is grateful for the following additional support: a grant from the Leverhulme Trust, a Royal Society Wolfson Research Merit Award, a Royal Society Leverhulme Senior Research Fellowship, and a grant from the Air Force Office of Scientific Research, Air Force Material Command, USAF (number FA8655-10-1-3088). He is also pleased to thank the American Institute of Mathematics for hospitality during a visit where this work started.
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Conrey, B., Keating, J.P. (2015). Moments of Zeta and Correlations of Divisor-Sums: II. In: Alaca, A., Alaca, Ş., Williams, K. (eds) Advances in the Theory of Numbers. Fields Institute Communications, vol 77. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3201-6_3
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