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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
