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A study on multiple zeta values from the viewpoint of zeta-functions of root systems
multiple zeta values zeta-functions of root systems Number Theory
2012/5/9
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Za...
On Mordell-Tornheim sums and multiple zeta values
Tornheim series Witten zeta function Euler sums multiple harmonic series multiple zeta values
2012/5/9
We prove that any Mordell-Tornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, i...
Sums of alternating products of Riemann zeta values and solution of a Monthly problem
first Stieltjes constant Euler constant Riemann zeta function digamma function
2011/7/26
Abstract: We solve problem 11585 proposed by B. Burdick, AMM June-July 2011 {bf 118} (6), p. 558 for the sum of certain products of Riemann zeta function values. We further point out an alternating su...
Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values
Bell polynomials Euler's constant zeta values
2010/11/22
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zet...