Density of rational points on cyclic covers of ℙ n
Ritabrata Munshi
Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 335-341.

Nous obtenons une majoration de la densité des points rationnels sur les revêtements cycliques de ℙ n . Quand n→∞ notre estimation tend vers la majoration conjecturale de Serre.

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.

@article{JTNB_2009__21_2_335_0,
     author = {Ritabrata Munshi},
     title = {Density of rational points on cyclic covers of $\mathbb{P}^n$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {335--341},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {2},
     year = {2009},
     doi = {10.5802/jtnb.674},
     zbl = {1187.14026},
     mrnumber = {2541429},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2009__21_2_335_0/}
}
Ritabrata Munshi. Density of rational points on cyclic covers of $\mathbb{P}^n$. Journal de Théorie des Nombres de Bordeaux, Tome 21 (2009) no. 2, pp. 335-341. doi : 10.5802/jtnb.674. https://jtnb.centre-mersenne.org/item/JTNB_2009__21_2_335_0/

[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. | MR 1032922 | Zbl 0679.14008

[2] N. Broberg, Rational points on finite covers of ℙ 1 and ℙ 2 . J. Number Theory 101 (2003), 195–207. | MR 1979659 | Zbl 1054.14024

[3] S.D. Cohen, The distribution of Galois groups and Hilbert’s irreducibility theorem. Proc. London Math. Soc. (3) 43 (1981), 227–250. | MR 628276 | Zbl 0484.12002

[4] P. Deligne, La conjecture de Weil. I. Inst. Hautes Études Sci. Publ. Math. No. 43 (1974), 273–307. | Numdam | MR 340258 | Zbl 0287.14001

[5] J. Franke; Y.I. Manin; Y. Tschinkel, Rational points of bounded height on Fano varieties. Invent. Math. 95 (1989), 421–435. | MR 974910 | Zbl 0674.14012

[6] D.R. Heath-Brown, The square sieve and consecutive square-free numbers. Math. Ann. 266 (1984), 251–259. | MR 730168 | Zbl 0514.10038

[7] D.R. Heath-Brown, The density of rational points on curves and surfaces. Ann. of Math. (2) 155 (2002), 553–595. | MR 1906595 | Zbl 1039.11044

[8] N. Katz, Estimates for nonsingular multiplicative character sums. Int. Math. Res. Not. (2002), 333–349. | MR 1883179 | Zbl 1028.11075

[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. | MR 2359542 | Zbl 1145.11084

[10] J-P. Serre, Lectures on the Mordell-Weil theorem. Friedr. Vieweg & Sohn, Braunschweig (1989). | MR 1002324 | Zbl 0676.14005