@incollection{AST_1995__228__165_0, author = {Mazur, B.}, title = {Speculations about the topology of rational points: an up-date}, booktitle = {Columbia university number theory seminar - New-York, 1992}, series = {Ast\'erisque}, pages = {165--181}, publisher = {Soci\'et\'e math\'ematique de France}, number = {228}, year = {1995}, mrnumber = {1330932}, zbl = {0851.14009}, language = {en}, url = {http://www.numdam.org/item/AST_1995__228__165_0/} }
TY - CHAP AU - Mazur, B. TI - Speculations about the topology of rational points: an up-date BT - Columbia university number theory seminar - New-York, 1992 AU - Collectif T3 - Astérisque PY - 1995 SP - 165 EP - 181 IS - 228 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_1995__228__165_0/ LA - en ID - AST_1995__228__165_0 ER -
%0 Book Section %A Mazur, B. %T Speculations about the topology of rational points: an up-date %B Columbia university number theory seminar - New-York, 1992 %A Collectif %S Astérisque %D 1995 %P 165-181 %N 228 %I Société mathématique de France %U http://www.numdam.org/item/AST_1995__228__165_0/ %G en %F AST_1995__228__165_0
Mazur, B. Speculations about the topology of rational points: an up-date, dans Columbia university number theory seminar - New-York, 1992, Astérisque, no. 228 (1995), pp. 165-181. http://www.numdam.org/item/AST_1995__228__165_0/
1. [A-J] Uniform distribution of integral points on -dimensional spheres via modular forms. Journal of Number Theory 11 (1979) 218-238 | DOI | MR | Zbl
, :2. [B-M] Sur le nombre des points rationnels de hauteur bornée des variétés algébriques. Math. Ann. 286 (1990) 27-43 | DOI | EuDML | MR | Zbl
, :3. [B 1] Homogeneous forms of odd degree in a large number of variables. Mathematika 4 (1957) 102-105 | DOI | MR | Zbl
:4. [B 2] Forms in many variables. Proc. Roy. Soc. Ser. A 265 (1962) 245-263 | DOI | MR | Zbl
:5. [Bu] Remarques sur la stabilité en arithmétique. International Math. Research Notices (1992) no. 6 in Duke Math. J. 66 (1992) 117-127 | MR | Zbl
:6. [C-S] Canonical heights on varieties with morphisms. Preprint (1993) | Numdam | MR | Zbl
, :7. [Ca-N] Valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme II, Amer. J. of Math. 106 (1985) 255-299 | DOI | MR | Zbl
:8. [CT 1] Arithmétique des variétés rationnelles et problèmes birationnels. Proc. Int. Cong. Math. Berkeley Ca. (1986) 641-653 | MR | Zbl
:9. Surfaces rationnelles fibrées en coniques de degré . Séminaire de Théorie des Nombres, Paris 1988-1989. Birkhäuser, Boston-Basel-Berlin (1990) 43-55 | MR | Zbl
:10. [CT-Sa 1] Sur le principle de Hasse et l'approximation faible, et sur une hypothèse de Schinzel. Acta Arithmetica XLI.1 (1982) 33-53 | DOI | EuDML | MR | Zbl
, :11. [CT-Sa 2] La descente sur les variétés rationnelles II. Duke Math. J. 54 (1987) 375-492 | DOI | MR | Zbl
, :12. [CT-S-SD] Intersections of two quadrics and Châtelet surfaces, II, J. für die reine und angew. Math. 374 (1987) 72-168 | EuDML | MR | Zbl
, , :13. [CT-SD] Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties. Preprint (1992) | MR | Zbl
, :14. [C-V] On sums of three integral cubes. Preprint (1992) | MR | Zbl
, :15. [C-T] Arithmetic on singular Del Pezzo surfaces, Proc. London Math. Soc. 57 (1988) 25-87 | DOI | MR | Zbl
, :16. [D-W] The adelic zeta-function associated with the space of binary cubic forms II: Local theory. Journal für die reine und der angew. Math. 386 (1988) 116-138 | MR
, :17. [D-L] Homogeneous additive equations. Proc. Roy. Soc. Ser. A 274 (1963) 443-460 | DOI | MR | Zbl
, :18. [D] Hyperbolic distribution problems and half-integral weight Maass forms. Inv. Math. 92 (1988) 73-90 | DOI | EuDML | MR | Zbl
:19. [D-R-S] Density of integer points on affine homogeneous varieties. Preprint (1991) | MR | Zbl
, , :20. [D-S-P] Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids. Inv. Math. 99 (1990) 49-57 | DOI | EuDML | MR | Zbl
, :21. [F] Invariants of divisor classes for the curves in an -adic cyclotomic field. Tr. Mat. Inst. Steklova 64 (1961) 284-293 | MR | Zbl
:22. [F-M & T] Rational points of bounded height on Fano varieties. Inv. Math. 95 (1989) 421-435 | DOI | EuDML | MR | Zbl
, , :23. [F-G] Application of spherical functions to a certain problem in the theory of quadratic forms. J. Sov. Math. 38 (1987) 2054-2060 | DOI | MR | Zbl
, :24. [G-G] Computing the Mordell-Weil rank of Jacobians of curves of genus two. Preprint (1991) | MR | Zbl
, :25. [G-R] Some results on the Mordell-Weil group of the jacobian of the Fermat curve. Inv. Math. 44 (1978) 201-224 | DOI | EuDML | MR | Zbl
, :26. [H-B] The density of zeros of forms for which weak approximation fails. Mathematics of Computation 59 (1992) 613-623 | DOI | MR | Zbl
:27. [Hi] Triangulations of algebraic sets. Proc. Sympos. Pure Math. 29 A.M.S. Providence, R.I. (1975) 165-185 | DOI | MR | Zbl
:28. [Ho] On nonary cubic forms: I. Journal für die reine und der angew. Math. 386 (1988) 32-98 | EuDML | MR | Zbl
:On nonary cubic forms: II. Journal für die reine und der angew. Math. 415 (1991) 95-165 | EuDML | MR | Zbl
:29. [Ig] Forms of higher degree, Tata Institute of Fundamental Research, Bombay (1978) | MR | Zbl
:30. [Iw] Fourier coefficients of modular forms of half integral weight. Inv. Math. 87 (1987) 385-401 | DOI | EuDML | MR | Zbl
:31. [K] Euler systems, pp. 435-483 in: The Grothendieck Festschrift II, Progress in Mathematics 87, Birkhäuser, Boston-Basel-Berlin (1990) | MR | Zbl
:32. [K-R] Simple factors in the jacobian of a Fermat curve. Can. J. Math. 30 (1978) 1183-1205 | DOI | MR | Zbl
, :33. [K-W] Topology of rational points on isotrivial elliptic surfaces. To appear: in Int. Math. Research Notices, in Duke Math. J. (1993) | MR | Zbl
, :34. [Licht] On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials. Compositio Math. 80 (1991) 337-354 | EuDML | Numdam | MR | Zbl
:35. [Linn] Ergodic properties of algebraic fields. Springer-Verlag 1968 | DOI | MR | Zbl
:36. [Lo] Triangulation of semi-analytic sets. Ann. Scuo. Norm. Pisa 18 (1964) 449-474 | EuDML | Numdam | MR | Zbl
:37. [Mal] On representations of integers by positive quadratic forms. Trudy V.A. Steklov Math. Inst. AN SSSR 65 (1962) 1-212 | MR | Zbl
:38. [Mn 1] Cubic Forms, algebra, geometry, arithmetic (2nd Ed.) North-Holland (1986) | MR | Zbl
:39. [Ms 2] Algebraic Varieties With Many Rational Points, Lecture Notes, MIT (1990)
:40. [Mn 3] Notes on the arithmetic of Fano threefolds, Composito Mathematica 85 (1993) 37-55 | EuDML | Numdam | MR | Zbl
:41. [M-Tsch] Points of bounded height on Del Pezzo surfaces. Preprint no. 655. Univ. of Utrecht (1991) | Numdam | MR | Zbl
, :42. [Mz 1] The topology of rational points. Journ. Exp. Math. 1 (1992) 35-45 | EuDML | MR | Zbl
:43. [Mz 2] Questions of decidability and undecidability in Number Theory. To appear: Journal of Symbolic Logic | MR | Zbl
:44. [Mc] The arithmetic of Fermat curves. Math. Ann. 294 (1992) 503-511 | DOI | EuDML | MR | Zbl
:45. [Pe] Hauteurs et nombres de Tamagawa sur les variétés de Fano, preprint | Zbl
:46. [P] Über die Gleichverteilung von Gitterpunkten auf -dimensionalen Ellipsoiden. Acta Arith. 5 (1957) 227-257 | DOI | EuDML | MR | Zbl
:47. [R] Variation of the root number in families of elliptic curves. Preprint (1992) | Numdam | MR | Zbl
:48. [Sa] Croissance de certaines séries de Dirichlet et applications. Journal für die reine und der angew. Math. 367 (1986) 139-154 | EuDML | MR | Zbl
:49. [Sch] The density of integer points on homogeneous varieties. Acta Mathematica 154 (1985) 243-296 | DOI | MR | Zbl
:50. [Se] Lectures on the Mordell-Weil Theorem. Aspects of Math. 15 Vieweg (1989) | MR | Zbl
:51. [Si 1] Rational points on surfaces: a new canonical height. Inv. Math. 105 (1991) 347-373 | DOI | EuDML | MR | Zbl
:52. [Si 2] Counting integer and rational points on varieties. Preprint (1991); in this volume. | Numdam | MR | Zbl
:53. [S-D] Counting rational points on cubic surfaces. Preprint 1993 | MR | Zbl
:54. [Th] An asymptotic estimate for heights of algebraic subspaces. PhD Thesis, Univ. of Colorado (1990) | MR
:55. [Tsch] Arithmetic of algebraic surfaces. M.I.T. PhD thesis (1992) | MR
:56. [We] - surfaces with Picard number . Arch. Math. 50 (1988) 73-82 | DOI | MR | Zbl
:57. [Wr] The adelic zeta-function associated with the space of binary cubic forms II: Global theory. Global theory Math. Ann. 270 (1985) 503-534 | EuDML | MR | Zbl
:58. [W-Y] Prehomogeneous vector spaces and field extensions. Inv. Math. 110 (1992) 283-314 | DOI | EuDML | MR | Zbl
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