Counting rational points near planar curves

• Autorzy: Ayla Gafni
• Języki publikacji: EN

Abstrakty

EN

We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².

Kategorie tematyczne

• 11K60: Diophantine approximation
• 11J83: Metric theory
• 11J13: Simultaneous homogeneous approximation, linear forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 1
• Strony: 91-100

Daty

wydano

2014

Twórcy

autor

Ayla Gafni

• Department of Mathematics, Pennsylvania State University, 109 McAllister Bldg, University Park, PA 16802, U.S.A.

Identyfikatory

DOI

10.4064/aa165-1-5