# On the Primitive Circle Problem

@article{Wu2002OnTP, title={On the Primitive Circle Problem}, author={Jie Wu}, journal={Monatshefte f{\"u}r Mathematik}, year={2002}, volume={135}, pages={69-81} }

Abstract. We prove that under the Riemann hypothesis one has for any ɛ > 0, This improves a result of Zhai and Cao, which requires 11/30 in place of 221/608.

#### 23 Citations

The Riemann Hypothesis

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We prove some analogues of planar lattice point problems replacing R2 by the Poincaré model of the hyperbolic plane and using the orbit of a point under the modular group instead of the lattice… Expand

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We consider the analog of visibility problems in hyperbolic plane (represented by Poincaré half-plane model ℍ), replacing the standard lattice ℤ × ℤ by the orbitz = i under the full modular group… Expand

Ω-estimates for a class of arithmetic error terms

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- Mathematical Proceedings of the Cambridge Philosophical Society
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Abstract The main aim of this paper is to present a general method of proving Ω-estimates for a class of arithmetic error terms. We assume that error terms in question are boundary values of harmonic… Expand

Oscillations of a given size of some arithmetic error terms

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A general method of estimating the number of oscillations of a given size of arithmetic error terms is developed. Special attention is paid to the remainder terms in the prime number formula, in the… Expand

Almost primes of the form ⌊pc⌋

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Abstract Let P c = ( ⌊ p c ⌋ ) p ∈ P with c > 1 and c ∉ N , where P is the set of prime numbers, and ⌊ ⋅ ⌋ is the floor function. We show that for every such c there are infinitely many members of P… Expand

Primitive lattice points in planar domains

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(Zhai [21]). The smoothness assumptions on C vary in these papers. Indeed, Zhai’s curves C are only piecewise smooth, and D is not necessarily convex; but Zhai imposes Diophantine approximation… Expand

Mean Square Estimate for Primitive Lattice Points in Convex Planar Domains

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Farey Statistics in Time n^{2/3} and Counting Primitive Lattice Points in Polygons

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We present algorithms for computing ranks and order statistics in the Farey sequence, taking time O (n^{2/3}). This improves on the recent algorithms of Pawlewicz [European Symp. Alg. 2007], running… Expand