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Zbl 0755.11026
Zhang, Wenpeng
On the several identities of Riemann zeta-function. (English)
[J] Chin. Sci. Bull. 36, No.22, 1852-1856 (1991). ISSN 1001-6538; ISSN 1861-9541/e

The author records various identities, as an example: If an integer $n>4$, then $$24\sum\sb{a+b+c+d=n} \zeta(2a)\zeta(2b)\zeta(2c)\zeta(2d)= (n+1)(2n+1)(2n+3) \zeta(2n)-48n\zeta(2)\zeta(2n-2).\tag1$$ Also, he points out a correction in the formula $$\multline 96\sum\sb{a+b+c+d+e=n} \zeta(2a)\zeta(2b)\zeta(2c)\zeta(2d)\zeta(2e)= \\ =(n+1)(n+2)(2n+1)(2n+3) \zeta(2n)-60n(n+1)\zeta(2)\zeta(2n-2)+ 144\zeta\sp 2(2) \zeta(2n-4) \endmultline \tag2 $$ in which the constant 144 should be 216. The formula (2) was obtained by the reviewer in [Indian J. Pure Appl. Math. 18, 794-800 (1987; Zbl 0625.10031)]. This correction is trivial and it can be seen easily from the equation (3.1.6) of the above paper.\par In the following paper [Indian J. Pure Appl. Math. 18, 891-895 (1987; Zbl 0635.10036)] much more has been proved by the reviewer jointly with {\it K. Ramachandra}. The method of the paper under review is not very different from the above mentioned paper.
[A.Sankaranarayanan (Bombay)]

MSC 2000:: *11M06 Riemannian zeta-function and Dirichlet L-function

Keywords: identities; Riemann zeta-function

Citations: Zbl 0625.10031; Zbl 0635.10036

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