Moments of the Riemann zeta-function at its relative extrema on the critical line

Details Moments of the Riemann zeta-function at its relative extrema on the critical line Moments of the Riemann zeta-function at its relative extrema on the critical line

2011-06-06

arxiv.org/abs/1106.1154v1

Mathematics

Number Theory

12 pages, to appear in Bull. Lond. Math. Soc

Scientific paper

Assuming the Riemann hypothesis, we obtain upper and lower bounds for moments
of the Riemann zeta-function averaged over the extreme values between its zeros
on the critical line. Our bounds are very nearly the same order of magnitude.
The proof requires upper and lower bounds for continuous moments of derivatives
of Riemann zeta-function on the critical line.

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