科研之友
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摘要
Keating and Snaith modeled the Riemann zeta-function zeta(s) by characteristic polynomials of random N x N unitary matrices, and used this to conjecture the asymptotic main term for the 2k-th moment of zeta(1/2 + it) when k > -1/2. However, an arithmetical factor, widely believed to be part of the leading term coefficient, had to be inserted in an ad hoc manner. Gonek, Hughes and Keating later developed a hybrid formula for zeta(s) that combines a truncation of its Euler product with a product over its zeros. Using it, they recovered the moment conjecture of Keating and Snaith in a way that naturally includes the arithmetical factor. Here we use the hybrid formula to recover a conjecture of Hughes, Keating and O'Connell concerning the discrete moments of the derivative of the Riemann zeta-function averaged over the zeros of zeta(s), incorporating the arithmetical factor in a natural way.
- 出版日期2015-5
