On the occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function |
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Authors: | H Kösters |
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Institution: | Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany |
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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 (2003, 2005) CFKRS1] and CFKRS2]. |
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Keywords: | Riemann zeta function Mean value theorem Correlation Sine kernel Random matrix theory |
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