H.E. Boos1 Institute for High Energy Physics Protvino, 142284, Russia V.E. Korepin 2 C.N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony Brook, NY 11794{3840, USA Abstract Riemann zeta function is an important object of number theory. We argue that it is related to Heisenberg spin 1/2 anti-ferromagnet. In the XXX spin chain we study the probability of f...

In this paper, we will give a certain formula for the Riemann zeta function that expresses the Riemann zeta function by an infinte series consisting of KBessel functions. Such an infinite series expression can be regarded as an analogue of the Chowla-Selberg formula. Roughly speaking, the Chowla-Selberg formula is the formula that expresses the Epstein zeta-function by an infinite series consis...

ABSTRACT Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37-52, 2007] and Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13-25, 1997], the main objective in this paper is to present a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associa...

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 establish this occurrence rigorously for the shifted second moment and, under some constraints on the shifts, for the shifted fourth moment. Our proofs of these results closely follow the classical proofs for the non-shifted moments ...

We define the field F1 of one element as a λ-ring Z with the canonical λ-structure. We show that we can calculate the Riemann zeta function of integers in two ways: the first, geometrical, as the zeta function of the affine line F1[x] over F1 and the second, categorical, using a suitable category of modules over F1.

Series acceleration formulas are obtained for Dirichlet series with periodic coefficients. Special cases include Ramanujan’s formula for the values of the Riemann zeta function at the odd positive integers exceeding two, and related formulas for values of Dirichlet L-series and the Lerch zeta function.

New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to...

Ž . Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator the Riemann operator with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 11.25.M; 05.45.M; 02.10.L For a long time a challenge for mathematical physics has been and is s...