The remainder terms aspect of the theory of the Riemann zeta-function

Ka-Lam Kueh

Vol. 150 (1991), No. 2, 341–358

DOI: 10.2140/pjm.1991.150.341

Abstract

Assuming the Riemann hypothesis for Riemann zeta-function ζ(s), let R(u) and S(t) denote the remainder terms for the prime number theorem (suitably normalized) and the zero counting formula for ζ(s) respectively. We analyze the relation between R(u) and S(t), which generalizes A. Guinand’s work.

Mathematical Subject Classification 2000

Primary: 11M26

Secondary: 11M06

Milestones

Received: 23 January 1989

Revised: 25 October 1990

Published: 1 October 1991