# Search Results

## You are looking at 1 - 1 of 1 items for

• Author or Editor: A. Ivić
• All content
Clear All Modify Search

# Some remarks on the moments of $$\left| {\varsigma \left( {\tfrac{1} {2} + it} \right)} \right|$$ in short intervals

Acta Mathematica Hungarica
Author: A. Ivić

## Abstract

Some new results on power moments of the integral

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$J_k (t,G) = \frac{1} {{\sqrt {\pi G} }}\int_{ - \infty }^\infty { \left| {\varsigma \left( {\tfrac{1} {2} + it + iu} \right)} \right|^{2k} } e^{ - (u/G)^2 } du$$ \end{document}
(tT, T ɛGT, κ ∈ N) are obtained when κ = 1. These results can be used to derive bounds for moments of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left| {\varsigma \left( {\tfrac{1} {2} + it} \right)} \right|$$ \end{document}
.

Restricted access