Arkiv för Matematik

  • Ark. Mat.
  • Volume 53, Number 2 (2015), 303-315.

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

Matti Jutila

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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).

Article information

Source
Ark. Mat., Volume 53, Number 2 (2015), 303-315.

Dates
Received: 21 March 2014
Revised: 28 April 2014
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802711

Digital Object Identifier
doi:10.1007/s11512-014-0204-9

Mathematical Reviews number (MathSciNet)
MR3391173

Zentralblatt MATH identifier
06484297

Rights
2014 © Institut Mittag-Leffler

Citation

Jutila, Matti. Riemann’s zeta-function and the divisor problem. III. Ark. Mat. 53 (2015), no. 2, 303--315. doi:10.1007/s11512-014-0204-9. https://projecteuclid.org/euclid.afm/1485802711


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References

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