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Density of rational points on cyclic covers of ℙ n

Ritabrata Munshi[1]

  • [1] Rutgers University 110, Frelinghuysen Road Piscataway NJ 08854, USA

Journal de Théorie des Nombres de Bordeaux (2009)

  • Volume: 21, Issue: 2, page 335-341
  • ISSN: 1246-7405

Abstract

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We obtain upper bound for the density of rational points on the cyclic covers of ℙ n . As n → ∞ our estimate tends to the conjectural bound of Serre.

How to cite

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Munshi, Ritabrata. "Density of rational points on cyclic covers of $\mathbb{P}^n$." Journal de Théorie des Nombres de Bordeaux 21.2 (2009): 335-341. <http://eudml.org/doc/10884>.

@article{Munshi2009,
abstract = {We obtain upper bound for the density of rational points on the cyclic covers of $\mathbb\{P\}^n$. As $n\rightarrow \infty $ our estimate tends to the conjectural bound of Serre.},
affiliation = {Rutgers University 110, Frelinghuysen Road Piscataway NJ 08854, USA},
author = {Munshi, Ritabrata},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {cyclic cover; rational points; height; counting function},
language = {eng},
number = {2},
pages = {335-341},
publisher = {Université Bordeaux 1},
title = {Density of rational points on cyclic covers of $\mathbb\{P\}^n$},
url = {http://eudml.org/doc/10884},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Munshi, Ritabrata
TI - Density of rational points on cyclic covers of $\mathbb{P}^n$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 2
SP - 335
EP - 341
AB - We obtain upper bound for the density of rational points on the cyclic covers of $\mathbb{P}^n$. As $n\rightarrow \infty $ our estimate tends to the conjectural bound of Serre.
LA - eng
KW - cyclic cover; rational points; height; counting function
UR - http://eudml.org/doc/10884
ER -

References

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  1. V.V. Batyrev; Y.I. Manin, Sur le nombre des points rationnels de hauteur borné des variétés algébriques. Math. Ann. 286 (1990), 27–43. Zbl0679.14008MR1032922
  2. N. Broberg, Rational points on finite covers of ℙ 1 and ℙ 2 . J. Number Theory 101 (2003), 195–207. Zbl1054.14024MR1979659
  3. S.D. Cohen, The distribution of Galois groups and Hilbert’s irreducibility theorem. Proc. London Math. Soc. (3) 43 (1981), 227–250. Zbl0484.12002MR628276
  4. P. Deligne, La conjecture de Weil. I. Inst. Hautes Études Sci. Publ. Math. No. 43 (1974), 273–307. Zbl0287.14001MR340258
  5. J. Franke; Y.I. Manin; Y. Tschinkel, Rational points of bounded height on Fano varieties. Invent. Math. 95 (1989), 421–435. Zbl0674.14012MR974910
  6. D.R. Heath-Brown,The square sieve and consecutive square-free numbers. Math. Ann. 266 (1984), 251–259. Zbl0514.10038MR730168
  7. D.R. Heath-Brown, The density of rational points on curves and surfaces. Ann. of Math. (2) 155 (2002), 553–595. Zbl1039.11044MR1906595
  8. N. Katz, Estimates for nonsingular multiplicative character sums. Int. Math. Res. Not. (2002), 333–349. Zbl1028.11075MR1883179
  9. N. Katz, Estimates for nonsingular mixed character sums. Int. Math. Res. Not. (2007), vol. 2007, article ID rnm069, 19 pages, doi:10.1093/imrn/rnm069. Zbl1145.11084MR2359542
  10. J-P. Serre, Lectures on the Mordell-Weil theorem. Friedr. Vieweg & Sohn, Braunschweig (1989). Zbl0676.14005MR1002324

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