A uniform version of Jarník's theorem

Alain Plagne

Acta Arithmetica (1999)

  • Volume: 87, Issue: 3, page 255-267
  • ISSN: 0065-1036

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Alain Plagne. "A uniform version of Jarník's theorem." Acta Arithmetica 87.3 (1999): 255-267. <http://eudml.org/doc/207220>.

@article{AlainPlagne1999,
author = {Alain Plagne},
journal = {Acta Arithmetica},
keywords = {strictly convex curve; integer points; Farey fractions; lattice points; sequence of real numbers; convex curve},
language = {eng},
number = {3},
pages = {255-267},
title = {A uniform version of Jarník's theorem},
url = {http://eudml.org/doc/207220},
volume = {87},
year = {1999},
}

TY - JOUR
AU - Alain Plagne
TI - A uniform version of Jarník's theorem
JO - Acta Arithmetica
PY - 1999
VL - 87
IS - 3
SP - 255
EP - 267
LA - eng
KW - strictly convex curve; integer points; Farey fractions; lattice points; sequence of real numbers; convex curve
UR - http://eudml.org/doc/207220
ER -

References

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  1. [1] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), 337-357. Zbl0718.11048
  2. [2] G. Grekos, Sur le nombre de points entiers d'une courbe convexe, Bull. Sci. Math. (2) 112 (1988), 235-254. Zbl0657.10031
  3. [3] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, 1979. Zbl0423.10001
  4. [4] V. Jarník, Über die Gitterpunkte auf konvexen Kurven, Math. Z. 24 (1926), 500-518. 
  5. [5] H. Niederreiter, The distribution of Farey points, Math. Ann. 201 (1973), 341-345. Zbl0248.10013
  6. [6] J. Pila, Geometric postulation of a smooth function and the number of rational points, Duke Math. J. 63 (1991), 449-463. Zbl0763.11025
  7. [7] W. M. Schmidt, Integer points on curves and surfaces, Monatsh. Math. 99 (1985), 45-72. Zbl0551.10026
  8. [8] H. P. F. Swinnerton-Dyer, The number of lattice points on a convex curve, J. Number Theory 6 (1974), 128-135. Zbl0285.10020
  9. [9] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publication de l'Institut Élie Cartan, Nancy, 1990. 
  10. [10] A. M. Vershik, The limit shape of convex lattice polygons and related topics, Functional Anal. Appl. 28 (1994), 13-20. Zbl0848.52004

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