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On the several identities of Riemann zeta-function. (English) Zbl 0755.11026

The author records various identities, as an example: If an integer n>4, then

24 a+b+c+d=n ζ(2a)ζ(2b)ζ(2c)ζ(2d)=(n+1)(2n+1)(2n+3)ζ(2n)-48nζ(2)ζ(2n-2)·(1)

Also, he points out a correction in the formula

96 a+b+c+d+e=n ζ(2a)ζ(2b)ζ(2c)ζ(2d)ζ(2e)==(n+1)(n+2)(2n+1)(2n+3)ζ(2n)-60n(n+1)ζ(2)ζ(2n-2)+144ζ 2 (2)ζ(2n-4)(2)

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.

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 K. Ramachandra. The method of the paper under review is not very different from the above mentioned paper.

MSC:
11M06ζ(s) and L(s,χ)