Vol. 8, No. 3, 2019

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The mean square discrepancy in the circle problem

Steven M. Gonek and Alex Iosevich

Vol. 8 (2019), No. 3, 263–287
Abstract

We study the mean square of the error term in the Gauss circle problem. A heuristic argument based on the consideration of off-diagonal terms in the mean square of the relevant Voronoi-type summation formula leads to a precise conjecture for the mean square of this discrepancy.

Keywords
lattice points, circle problem, discrepancy estimates
Mathematical Subject Classification 2010
Primary: 11P21
Milestones
Received: 11 December 2018
Revised: 10 March 2019
Accepted: 4 April 2019
Published: 23 July 2019
Authors
Steven M. Gonek
Department of Mathematics
University of Rochester
Rochester, NY
United States
Alex Iosevich
Department of Mathematics
University of Rochester
Rochester, NY
United States