Vol. 98, No. 1, 1982

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ISSN: 0030-8730
On the order of ζ(1 2 + it) and Δ(R)

Grigori Abramovich Kolesnik

Vol. 98 (1982), No. 1, 107–122
Abstract

In this paper we obtain new estimates of ζ(12 + it), the value of the Riemann zeta-function on the critical line, and Δ(R), the remainder in the Dirichlet divisor problem.

The estimates are

ζ(1+ it) ≪ t35∕216+𝜀 for any 𝜀 > 0
2

and

Δ(R ) ≪ R35∕108+ 𝜀 for any 𝜀 > 0,

which improve previously known best results.

Mathematical Subject Classification
Primary: 10H25, 10H25
Secondary: 10H05
Milestones
Received: 5 May 1976
Published: 1 January 1982
Authors
Grigori Abramovich Kolesnik