Lattice points in a circle for generic unimodular shears

Dubi Kelmer

Type: Article

Publication Date: 2016-07-01

Citations: 1

DOI: https://doi.org/10.1142/s179304211750018x

Abstract

Given a unimodular lattice [Formula: see text] consider the counting function [Formula: see text] counting the number of lattice points of norm less than [Formula: see text], and the remainder [Formula: see text]. We give an elementary proof that the mean square of the remainder over the set of all shears of a unimodular lattice is bounded by [Formula: see text].

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (11)

Action	Title	Year	Authors
+	On the distribution of the number of lattice points inside a family of convex ovals	1992	Pavel Bleher
+ PDF Chat	Lattice counting for deformations of convex domains	2006	Yiannis N. Petridis John A. Toth
+ PDF Chat	Lattice points inside random ellipsoids	2004	Steve Hofmann Alex Iosevich D. Weidinger
+	Exponential Sums and Lattice Points III	2003	M. N. Huxley
+	The remainder in Weyl's law for random two-dimensional	2002	Yiannis N. Petridis Juraj Tóth
+	On the divisor and circle problems	1988	Henryk Iwaniec C. J. Mozzochi
+	Primes of the form [<i>n</i><sup><i>c</i></sup>]	1985	Grigori Kolesnik
+	On the average order of the lattice rest of a convex planar domain	1985	Werner Georg Nowak
+ PDF Chat	The mean lattice point discrepancy	1995	M. N. Huxley
+	Exponential Sums and Lattice Points II	1993	M. N. Huxley