We obtain upper bound for the density of rational points on the cyclic covers of . As our estimate tends to the conjectural bound of Serre.
Nous obtenons une majoration de la densité des points rationnels sur les revêtements cycliques de . Quand notre estimation tend vers la majoration conjecturale de Serre.
@article{JTNB_2009__21_2_335_0, author = {Munshi, Ritabrata}, 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 = {http://archive.numdam.org/articles/10.5802/jtnb.674/} }
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 SP - 335 EP - 341 VL - 21 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.674/ DO - 10.5802/jtnb.674 LA - en ID - JTNB_2009__21_2_335_0 ER -
%0 Journal Article %A Munshi, Ritabrata %T Density of rational points on cyclic covers of $\mathbb{P}^n$ %J Journal de théorie des nombres de Bordeaux %D 2009 %P 335-341 %V 21 %N 2 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.674/ %R 10.5802/jtnb.674 %G en %F JTNB_2009__21_2_335_0
Munshi, Ritabrata. Density of rational points on cyclic covers of $\mathbb{P}^n$. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, pp. 335-341. doi : 10.5802/jtnb.674. http://archive.numdam.org/articles/10.5802/jtnb.674/
[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 | Zbl
[2] N. Broberg, Rational points on finite covers of and . J. Number Theory 101 (2003), 195–207. | MR | Zbl
[3] S.D. Cohen, The distribution of Galois groups and Hilbert’s irreducibility theorem. Proc. London Math. Soc. (3) 43 (1981), 227–250. | MR | Zbl
[4] P. Deligne, La conjecture de Weil. I. Inst. Hautes Études Sci. Publ. Math. No. 43 (1974), 273–307. | Numdam | MR | Zbl
[5] J. Franke; Y.I. Manin; Y. Tschinkel, Rational points of bounded height on Fano varieties. Invent. Math. 95 (1989), 421–435. | MR | Zbl
[6] D.R. Heath-Brown, The square sieve and consecutive square-free numbers. Math. Ann. 266 (1984), 251–259. | MR | Zbl
[7] D.R. Heath-Brown, The density of rational points on curves and surfaces. Ann. of Math. (2) 155 (2002), 553–595. | MR | Zbl
[8] N. Katz, Estimates for nonsingular multiplicative character sums. Int. Math. Res. Not. (2002), 333–349. | MR | Zbl
[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 | Zbl
[10] J-P. Serre, Lectures on the Mordell-Weil theorem. Friedr. Vieweg & Sohn, Braunschweig (1989). | MR | Zbl
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