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October 2015 Riemann’s zeta-function and the divisor problem. III
Matti Jutila
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Ark. Mat. 53(2): 303-315 (October 2015). DOI: 10.1007/s11512-014-0204-9

Abstract

In two earlier papers with the same title, we studied connections between Voronoi’s formula in the divisor problem and Atkinson’s formula for the mean square of Riemann’s zeta-function. Now we consider this correspondence in terms of segments of sums appearing in these formulae and show that a certain arithmetic conjecture concerning the divisor function implies best possible bounds for the classical error terms Δ(x) and E(T).

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Matti Jutila. "Riemann’s zeta-function and the divisor problem. III." Ark. Mat. 53 (2) 303 - 315, October 2015. https://doi.org/10.1007/s11512-014-0204-9

Information

Received: 21 March 2014; Revised: 28 April 2014; Published: October 2015
First available in Project Euclid: 30 January 2017

zbMATH: 06484297
MathSciNet: MR3391173
Digital Object Identifier: 10.1007/s11512-014-0204-9

Rights: 2014 © Institut Mittag-Leffler

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Vol.53 • No. 2 • October 2015
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