arXiv subjects
Publications and source records attributed to Isao Wakabayashi.
We investigate the distribution of zeros of the function $ζ_2(s,s)$, namely the function defined by putting $s_1=s_2=s$ in the Euler double zeta-function $ζ_2(s_1,s_2)$. Our theorems provide refinements of observations, obtained numerically in a previous paper by the first author and M. Shōji, with rigorous theoretical proofs.
We give explicit expressions (or at least an algorithm of obtaining such expressions) of the coefficients of the Laurent series expansions of the Euler-Zagier multiple zeta-functions at any integer points. The main tools are the Mellin-Barnes integral formula and the harmonic product formulas. The Mellin-Barnes integral formula is used in the induction process on the number of variables, and the harmonic product formula is used to show that the Laurent series expansion outside the domain of convergence can be obtained from that inside the domain of convergence.