Convolution of Riemann zeta-values
KANEMITSU, Shigeru ; TANIGAWA, Yoshio ; YOSHIMOTO, Masami
J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 1167-1177 / Harvested from Project Euclid
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In this note we are going to generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta-values of depth 2. Prior to this, we shall deduce the most well-known relation that expresses the sum $\sum_{j=1}^{m-2} \zeta(j+1)\zeta(m-j)$ in terms of $\zeta_2(1,m)$ .
Publié le : 2005-10-14
Classification:  Riemann zeta-values,  Euler-Zagier sum,  Mellin transform,  11M06,  11M41 
@article{1150287308,
     author = {KANEMITSU, Shigeru and TANIGAWA, Yoshio and YOSHIMOTO, Masami},
     title = {Convolution of Riemann zeta-values},
     journal = {J. Math. Soc. Japan},
     volume = {57},
     number = {4},
     year = {2005},
     pages = { 1167-1177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150287308}
}

KANEMITSU, Shigeru; TANIGAWA, Yoshio; YOSHIMOTO, Masami. Convolution of Riemann zeta-values. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp.  1167-1177. http://gdmltest.u-ga.fr/item/1150287308/