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Abstract: We present a new approach to obtaining the lower order terms for$n$-correlation of the zeros of the Riemann zeta function. Our approach isbased on the `ratios conjecture- of Conrey, Farmer, and Zirnbauer. Assuming theratios conjecture we prove a formula which explicitly gives all of the lowerorder terms in any order correlation. Our method works equally well for randommatrix theory and gives a new expression, which is structurally the same asthat for the zeta function, for the $n$-correlation of eigenvalues of matricesfrom UN.



Author: J.B.Conrey, N.C.Snaith

Source: https://arxiv.org/



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