On some conjectures and results for the Riemann zeta-function and Hecke series

Aleksandar Ivic

On some conjectures and results for the Riemann zeta-function and Hecke series

Number Theory 2007-05-23 v1

Authors: Aleksandar Ivic

Abstract

Some results and conjectures on $Z_2(s) = \int_1^\infty |\zeta(1/2+ix)|^4x^{-s}dx (\Re s > 1)$ are presented. Consequences of these conjectures regarding the eighth moment of $|\zeta(1/2+it)$ and the error term in the fourth moment of $|\zeta(1/2+it)$ are discussed.

Keywords

riemann zeta-function hecke series z_2(s) conjectures eighth moment error term

Cite

@article{arxiv.math/0311302,
  title  = {On some conjectures and results for the Riemann zeta-function and Hecke series},
  author = {Aleksandar Ivic},
  journal= {arXiv preprint arXiv:math/0311302},
  year   = {2007}
}

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