Moments of the Riemann zeta-function

Abstract

Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments in families of $L$-functions.

11 pages; Version 2 has some significant changes in the exposition

References in corpus (2)

• Lower bounds for moments of L-functions
• Extreme values of zeta and L-functions

Cited by in corpus (6)

• Upper bounds on L-functions at the edge of the critical strip
• On the correlation of shifted values of the Riemann zeta function
• Explicit Upper Bounds for L-functions on the critical line
• On the mean values of L-functions in orthogonal and symplectic families
• Mesoscopic fluctuations of the zeta zeros
• An analogue of Selberg's formula for Motohashi's product