On the distribution of rational points on certain Kummer surfaces

Atsushi Sato

Acta Arithmetica (1998)

  • Volume: 86, Issue: 1, page 1-16
  • ISSN: 0065-1036

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Atsushi Sato. "On the distribution of rational points on certain Kummer surfaces." Acta Arithmetica 86.1 (1998): 1-16. <http://eudml.org/doc/207178>.

@article{AtsushiSato1998,
author = {Atsushi Sato},
journal = {Acta Arithmetica},
keywords = {Batyrev-Manin conjecture; height; Kummer surface; rational points},
language = {eng},
number = {1},
pages = {1-16},
title = {On the distribution of rational points on certain Kummer surfaces},
url = {http://eudml.org/doc/207178},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Atsushi Sato
TI - On the distribution of rational points on certain Kummer surfaces
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 1
SP - 1
EP - 16
LA - eng
KW - Batyrev-Manin conjecture; height; Kummer surface; rational points
UR - http://eudml.org/doc/207178
ER -

References

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  1. [Ba] A. Baragar, Rational points on K3 surfaces in ℙ¹ × ℙ¹ × ℙ¹, Math. Ann. 305 (1996), 541-558. Zbl0877.14017
  2. [BM] V. V. Batyrev et Yu. I. Manin, Sur le nombre des points rationnels de hauteur borné des variétés algébriques, Math. Ann.. 286 (1990), 27-43. 
  3. [Bi] H. Billard, Propriétés arithmétiques d'une famille de surfaces K3, Compositio Math. 108 (1997), 247-275. 
  4. [CS1] G. S. Call and J. H. Silverman, Canonical heights on varieties with morphisms, Compositio Math.. 89 (1993), 163-205. Zbl0826.14015
  5. [CS2] G. S. Call and J. H. Silverman, Computing the canonical height on K3 surfaces, Math. Comp. 65 (1996), 259-290. Zbl0865.14020
  6. [K] E. Kani, Elliptic curves on abelian surfaces, Manuscripta Math. 84 (1994), 199-223. Zbl0821.14023
  7. [L] S. Lang, Fundamentals of Diophantine Geometry, Springer, New York, 1983. Zbl0528.14013
  8. [Mi] J. S. Milne, Abelian varieties, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, New York, 1986, 103-150. 
  9. [Mo] Y. Morita, Remarks on a conjecture of Batyrev and Manin, preprint. 
  10. [MS] Y. Morita and A. Sato, Distribution of rational points on hyperelliptic surfaces, Tôhoku Math. J. 44 (1992), 345-358. Zbl0840.14011
  11. [N] A. Néron, Quasi-fonctions et hauteurs sur les variétés abéliennes, Ann. of Math. 82 (1965), 249-331. Zbl0163.15205
  12. [Sc] S. H. Schanuel, Heights in number fields, Bull. Soc. Math. France 107 (1979), 433-449. Zbl0428.12009
  13. [S1] J. H. Silverman, Integral points on curves and surfaces, in: Number Theory (Ulm, 1987), H. P. Schlickewei and E. Wirsing (eds.), Lecture Notes in Math. 1380, Springer, New York, 1989, 202-241. 
  14. [S2] J. H. Silverman, Rational points on K3 surfaces: A new canonical height, Invent. Math. 105 (1991), 347-373. Zbl0754.14023
  15. [S3] J. H. Silverman, Counting integer and rational points on varieties, Astérisque 228 (1995), 223-236. Zbl0834.11029
  16. [W] L. Wang, Rational points and canonical heights on K3-surfaces in ℙ¹ × ℙ¹ × ℙ¹, in: Recent Developments in the Inverse Galois Problem, M. D. Fried et al. (eds.), Contemp. Math. 186, Amer. Math. Soc., Providence, R.I., 1995, 273-289. 

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