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

The Riemann Zeta-Function and the Sine Kernel