Power Moments of the Error Term for the Approximate Functional Equation of the Riemann Zeta-function

Isao Kiuchi

Publications de l'Institut Mathématique, _N_S_52 (1992) no. 66, p. 10 .

Résumé

Let $\zeta(s)$ be the Riemann zeta-function, $d(n)$ the number of positive divisors of the integer $n$, and $ R(s;t/2\pi) =\zeta^2(s) -\sum_{nłe t/2\pi}\!\!\!\strut'\enskip d(n)n^{-s} -\chi^2(s) \sum_{nłe t/2\pi}\!\!\!\strut'\enskip d(n)n^{s-1}, $ where $ \chi(s)=2^s\pi^{s-1}\sin(\frac12\pi s)\Gamma(1-s). $ We obtain the following power moment estimates: $ \int_1^T |R(\frac12+it;t/2\pi)|^A dt łl \cases T^{1-\frac14A+\vaeepsilon},0łe Ałe4,\\ 1,>4.\endcases $

Détail

Classification : 11M06