Some identities for the Riemann zeta-function

Details Some identities for the Riemann zeta-function Some identities for the Riemann zeta-function

2003-05-15

arxiv.org/abs/math/0305219v4

Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 14(2003), 20-25.

Mathematics

Number Theory

6 pages, no changes; TeX settings corrected

Scientific paper

Several identities for the Riemann zeta-function $\zeta(s)$ are proved. For
example, if $s = \sigma + it$ and $\sigma > 0$, then $$ \int_{-\infty}^\infty
|{(1-2^{1-s})\zeta(s)\over s}|^2dt = {\pi\over\sigma}(1 -
2^{1-2\sigma})\zeta(2\sigma). $$

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