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Lattice points in a circle and divisors in arithmetic progressions

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Abstract

Let A(x) denote the number of lattice points in the circle u2+v2≦x and define θ as the infimum of all reals λ for which\(\bar \bar A(x) = \pi x + 0(x^\lambda )\). The objective of this paper is to show that θ≦35/108 which improves upon all previously known results. This estimate is an immediate consequence of a surprisingly easy generalization of KOLESNIK's work on Dirichlet's divisor problem to divisor functions with respect to arithmetic progressions.

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  1. Institut für Mathematik der, Universität für Bodenkultur, Gregor Mendel - Straße 33, A-1180, Vienna, Austria

    Werner Georg Nowak

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  1. Werner Georg Nowak
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Nowak, W.G. Lattice points in a circle and divisors in arithmetic progressions. Manuscripta Math 49, 195–205 (1984). https://doi.org/10.1007/BF01168751

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