Riemann’s zeta-function and the divisor problem. III

Matti Jutila Department of Mathematics and Statistics, University of Turku

Number Theory mathscidoc:1701.24008

Arkiv for Matematik, 53, (2), 303-315, 2014.3
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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  title={Riemann’s zeta-function and the divisor problem. III},
  author={Matti Jutila},
  booktitle={Arkiv for Matematik},
Matti Jutila. Riemann’s zeta-function and the divisor problem. III. 2014. Vol. 53. In Arkiv for Matematik. pp.303-315. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640031599079.
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