The Riemann Zeta-Function and the Sine Kernel

DOI10.1016/J.JNT.2010.05.008arXiv0803.1141MaRDI QIDQ6208678

Publication date: 7 March 2008

Abstract: We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture that the sine kernel also occurs in connection with the higher (even) shifted moments and show that this conjecture is closely related to a recent conjecture by Conrey, Farmer, Keating, Rubinstein, and Snaith.

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Random matrices (algebraic aspects) (15B52) Relations with random matrices (11M50)

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