On quotients of Riemann zeta values at odd and even integer arguments

Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in ther...

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

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...

A Combinatorial Identity of Multiple Zeta Values with Even Arguments

Let ζ(s1, s2, · · · , sk;α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k 6 n, let E(2n, k;α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k;α).

Values of the Riemann zeta function at integers

Synchrotron Radiation Studies on Even-Odd and Odd-Even Nylons

Aliphatic polyamides derived from odd diamine or odd dicarboxylic acid units cannot adopt a conventional sheet structure when molecular chains have an all trans conformation. However, typical fiber diffraction patterns of this sheet structure were observed in several polyamides derived from odd units such as nylons 65 and 56. Consequently, a new structure based on the establishment of intermole...