Fonctions zêta des hauteurs

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1. S. J. Arakelov, Theory of intersections on the arithmetic surface. Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974), Vol. 1, 405–408. Canad. Math. Congress, Montreal, Que., 1975. Zbl0351.14003MR466150
2. V.V. Batyrev, Y.I. Manin, Sur les points rationnels de hauteur bornée des variétés algébriques. Math. Ann. 286 (1990), 27–43. Zbl0679.14008MR1032922
3. V.V. Batyrev, Y. Tschinkel, Rational points of bounded height on compactifications of anisotropic toric. Internat. Math. Res. Notices 12 (1995), 591–635. Zbl0890.14008MR1369408
4. V.V. Batyrev, Y. Tschinkel, Height Zeta functions of Toric Varieties, Algebraic geometry 5, Manin’s Festschrift. J. Math. Sci. 82 (1996), n${}^{\circ }$ 1, 3220–3239. Zbl0915.14013MR1423638
5. V.V. Batyrev, Y. Tschinkel, Manin’s Conjecture for Toric Varieties. J. of Algebraic Geometry 7 (1998), 15–53. Zbl0946.14009MR1620682
6. V.V. Batyrev, Y. Tschinkel, Tamagawa numbers of polarized algebraic varieties. Astérisque 251 (1998), 299–340. Zbl0926.11045MR1679843
7. G. Bhowmik, D. Essouabri, B. Lichtin, Meromorphic Continuation of Multivariable Euler Products and Applications. ArXiv math.NT/0502508, à paraître à Forum Math. Zbl1181.11057MR2367957
8. G. Bhowmik, J.-C. Schlage-Puchta, Natural boundaries of Dirichlet series. Functiones et Approximatio 37 (2007), 17–29. Zbl1146.30002MR2357306
9. R. de la Bretèche, Sur le nombre de points de hauteur bornée d’une certaine surface cubique singulière. Astérisque 251 (1998), 51–77. Zbl0969.14014MR1679839
10. R. de la Bretèche, Compter des points sur des variétés toriques. Journal of Number Theory 87 (2001), n${}^{\circ }$ 2, 315–331. Zbl1020.11045MR1824152
11. R. de la Bretèche, Nombre de points de hauteur bornée sur les surfaces de del Pezzo de degré 5. Duke Math. J. 113 (2002), n${}^{\circ }$ 3, 421–464. Zbl1054.14025MR1909606
12. R. de la Bretèche, T.D. Browning, On Manin’s conjecture for singular del Pezzo surfaces of degree four, I. Michigan Mathematical Journal 55 (2007), 51–80. Zbl1132.14019MR2320172
13. R. de la Bretèche, T.D. Browning, On Manin’s conjecture for singular del Pezzo surfaces of degree four, II. Math. Proc. Camb. Phil. Soc., à paraître. Zbl1132.14020
14. R. de la Bretèche, T.D. Browning, U. Derenthal, On Manin’s conjecture for a certain singular cubic surface. Annales scientifiques de l’ENS, $4$-ème série, 40 (2007), 1–50. Zbl1125.14008MR2332351
15. R. de la Bretèche, É. Fouvry, L’éclaté du plan projectif en quatre points dont deux conjugués. J. reine angew. Math. 576 (2004), 63–122. Zbl1065.11080MR2099200
16. R. de la Bretèche, Sir P. Swinnerton-Dyer, Fonction zêta des hauteurs associée à une certaine surface cubique. Bulletin de la SMF 135 (2007), 65–92. Zbl1207.11068MR2430199
17. T.D. Browning, The density of rational points on a certain singular cubic surface. J. Number Theory 119 (2006), 242–283. Zbl1119.11034MR2250046
18. T.D. Browning, An overview of Manin’s conjecture for del Pezzo surfaces. Analytic number theory - A tribute to Gauss and Dirichlet (Goettingen, 20th June - 24th June, 2005), Clay Mathematics Proceedings 7 (2007), 39–56. Zbl1134.14017MR2362193
19. A. Chambert-Loir, Y. Tschinkel, Yuri Points of bounded height on equivariant compactifications of vector groups, I Compositio Math. 124 (2000), no. 1, 65–93. Zbl0963.11033MR1797654
20. A. Chambert-Loir, Y. Tschinkel, Points of bounded height on equivariant compactifications of vector groups, II. J. Number Theory 85 (2000), no. 2, 172–188. Zbl0963.11034MR1802710
21. A. Chambert-Loir, Y. Tschinkel, Fonctions zêta des hauteurs des espaces fibrés. Rational points on algebraic varieties, 71–115, Progr. Math. 199, Birkhäuser, Basel, 2001. Zbl1077.14524MR1875171
22. A. Chambert-Loir, Y. Tschinkel, On the distribution of points of bounded height on equivariant compactifications of vector groups. Invent. Math. 148 (2002), 421–452. Zbl1067.11036MR1906155
23. J.-L. Colliot-Thélène, J.-J. Sansuc, La descente sur les variétés rationnelles. Journée de géométrie algébrique d’Angers (1979) (A. Beauville, ed.) Sijthoff, Noordhoff, Alphen aan den Rijn, 1980, 223–237. Zbl0451.14018MR605344
24. J.-L. Colliot-Thélène, J.-J. Sansuc, La descente sur les variétés rationnelles, II. Duke Math. J. 54 (1987), no 2, 375–492. Zbl0659.14028MR899402
25. U. Derenthal, Manin’s conjecture for a cubic surface. ArXiv :math.NT/0504016, (2005). 
26. U. Derenthal, Y. Tschinkel, Universal torsors over Del Pezzo surfaces and rational points. « Equidistribution in Number theory, An Introduction », (A. Granville, Z. Rudnick eds.), 169–196, NATO Science Series II 237, Springer, (2007). Zbl1143.14017MR2290499
27. D. Essouabri, Prolongements analytiques d’une classe de fonction zêta des hauteurs et applications. Bull. Soc. Math. France 133 (2) (2005), 297–329. Zbl1081.14031MR2172269
28. E. Fouvry, Sur la hauteur des points d’une certaine surface cubique singulière. Astérisque 251 (1998), 31–49. Zbl0930.11044MR1679838
29. T. Estermann, On certain functions represented by Dirichlet series. Proc. London Math. Soc. 27 (1928), 433–448. Zbl54.0366.03
30. J. Franke, Y.I. Manin, Y. Tschinkel, Rational points of bounded height on Fano varieties. Invent. Math. 95 (1989), 421–435. Zbl0674.14012MR974910
31. A. Gorodnik, F. Maucourant, H. Oh, Manin’s conjecture on rational points of bounded height and adelic mixing. Annales scientifiques de l’École Normale Supérieure, série 4, 41, fascicule 3 (2008), 385–437. Zbl1161.14015MR2482443
32. B. Hassett, Y. Tschinkel, Universal torsors and Cox rings. Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), 149–173, Progr. Math. 226, Birkhäuser, 2004. Zbl1077.14046MR2029868
33. R. Heath-Brown, The density of rational points on cubic surfaces. Acta Arith. 19 (1997), 17–30. Zbl0863.11021MR1438113
34. R. Heath-Brown, B.Z. Moroz, The density of Rational Points on the cubic surface $X_0^3=X_1{X}_2{X}_3$. Math. Proc. Camb. Phil. Soc. 125 (1999), n${}^{\circ }$ 3, 385–395. Zbl0938.11016MR1656797
35. M. N. Huxley, Exponential sums and the Riemann zeta function, V. Proc. London Math. Soc. (3) 90 (2005), no. 1, 1–41. Zbl1083.11052MR2107036
36. A. Ivić, The Riemann zeta-function. John Wiley, Sons Inc., New York, (1985). Zbl0556.10026MR792089
37. H. Iwaniec, C.J. Mozzochi, On the divisor and circle problems, J. Number Theory 29 (1988), no. 1, 60–93. Zbl0644.10031MR938870
38. N. Kurokawa, On the meromorphy of Euler products, I and II. Proc. London Math. Soc. (3) 53 (1986), no. 1, 1–47 and 209–236. Zbl0595.10031MR842154
39. Y. Manin, Y. Tschinkel, Points of bounded height on del Pezzo surfaces. Compositio Math. 85 (1993), n${}^{\circ }$ 3, 315–332. Zbl0782.14033MR1214451
40. E. Peyre, Hauteurs et nombres de Tamagawa sur les variétés de Fano. Duke Math. J. 79 (1995), 101–218. Zbl0901.14025MR1340296
41. E. Peyre, Terme principal de la fonction zêta des hauteurs et torseurs universels. Astérisque 251 (1998), 259–298. Zbl0966.14016MR1679842
42. E. Peyre, Points de hauteur bornée et géométrie des variétés (d’après Y. Manin et al.). Séminaire Bourbaki, Vol. 2000/2001. Astérisque 282 (2002), Exp. n${}^{\circ }$ 891, ix, 323–344. Zbl1039.11045MR1975184
43. E. Peyre, Points de hauteur bornée, topologie adélique et mesures de Tamagawa. Les XXIIèmes Journées Arithmetiques (Lille, 2001), J. Théor. Nombres Bordeaux 15 (2003), n${}^{\circ }$ 1, 319–349. Zbl1057.14031MR2019019
44. E. Peyre, Counting points on varieties using universal torsors. Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), 61–81, Progr. Math. 226, Birkhäuser Boston, Boston, MA, 2004. Zbl1201.11068MR2029862
45. P. Salberger, Tamagawa measures on universal torsors and points of bounded height on Fano varieties. Astérisque 251 (1998), 91–258. Zbl0959.14007MR1679841
46. M. du Sautoy, Zeta Functions of Groups and Natural Boundaries. Preprint 2000, 79 pages. Zbl1188.11047MR1765124
47. J.A. Shalika, Y. Tschinkel, Height zeta functions of equivariant compactifications of the Heisenberg group. Contributions to automorphic forms, geometry, and number theory, 743–771, Johns Hopkins Univ. Press, Baltimore, MD, 2004. Zbl1182.14013MR2058627
48. J.A. Shalika, R. Takloo-Bighash, Y. Tschinkel, Rational points on compactifications of semi-simple groups of rank 1. Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), 205–233, Progr. Math. 226, Birkhüser Boston, Boston, MA, 2004. Zbl1211.11080MR2029871
49. M. Strauch, Y. Tschinkel, Height zeta functions of twisted products. Math. Res. Lett. 4 (1997), n${}^{\circ }$ 2-3, 273–282. Zbl0918.11036MR1453059
50. M. Strauch, Y. Tschinkel, Height zeta functions of toric bundles over flag varieties. Selecta Math. (N.S.) 5 (1999), n${}^{\circ }$ 3, 325–396. Zbl1160.14302MR1723811
51. Sir P. Swinnerton-Dyer, Counting points on cubic surfaces II. Geometric methods in algebra and number theory, (Eds. F. Bogomolov and Y. Tschinkel), Progress in Mathematics 235, Birkhäuser, 2004. Zbl1127.11043MR2166089
52. G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres. Cours spécialisés, n${}^{\circ }$ 1, Société Mathématique de France (1995), xv + 457 pp. Zbl0880.11001MR1366197
53. E.C. Titchmarsh, The theory of the Riemann zeta-function. 2nd ed., revised by D.R. Heath-Brown. Oxford University Press, 1986. Zbl0601.10026MR882550
54. Y. Tschinkel, Lectures on height zeta functions of toric varieties. Geometry of toric varieties, 227–247, Sémin. Congr. 6, Soc. Math. France, Paris, 2002. Zbl1064.14018MR2075613
55. Y. Tschinkel, Fujita’s program and rational points. “Higher Dimensional Varieties and Rational Points”, (K. J. Böröczky, J. Kollár, T. Szamuely eds.), Bolyai Society Mathematical Studies 12, Springer Verl., 2003, 283–310. Zbl1112.14021MR2011749