This article is cited in 1 paper

New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem

O. V. Kolpakova

M. V. Lomonosov Moscow State University

Abstract: We obtain a new value of the Karatsuba constant in the multidimensional Dirichlet divisor problem. We also find a new value of the exponent of the main parameter in the estimate of the mean value of the remainder in a given asymptotics. The proof of the main statements is based on the derivation of a new estimate of the Carleson abscissa in the theory of the Riemann zeta function.

Keywords: Dirichlet divisor problem, Riemann zeta function, Karatsuba constant, Carleson exponent, Dirichlet series.

UDC: 511.335

Received: 28.12.2009

DOI: 10.4213/mzm9097

 English version: Mathematical Notes, 2011, 89:4, 504–518

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