Correlations of eigenvalues and Riemann zeros

Details Correlations of eigenvalues and Riemann zeros Correlations of eigenvalues and Riemann zeros

2008-03-19

arxiv.org/abs/0803.2795v1

Mathematics

Number Theory

Scientific paper

We present a new approach to obtaining the lower order terms for $n$-correlation of the zeros of the Riemann zeta function. Our approach is based on the `ratios conjecture' of Conrey, Farmer, and Zirnbauer. Assuming the ratios conjecture we prove a formula which explicitly gives all of the lower order terms in any order correlation. Our method works equally well for random matrix theory and gives a new expression, which is structurally the same as that for the zeta function, for the $n$-correlation of eigenvalues of matrices from U(N).

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