Crible et 3-rang des corps quadratiques

Annales de l'Institut Fourier

Volumn 46, Issue 4, 1996, Pages 909-949

  Belabas, Karim ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039545528     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1535     Document Type: Article

References (23)

1. R. BENEDETTI and J.-J. RISLER, Real algebraic and semi-algebraic sets, Hermann, 1990.
2. D.A. BUELL, Binary quadratic forms, Springer-Verlag, 1989.
3. H. COHEN and H. W. LENSTRA Jr., Heuristics on class groups of number fields, in Number Theory, Noordwijkerhout 1983, Lecture Notes in Math. no 1068, Springer-Verlag, 1984.
4. B. DATSKOVSKY and D. J. WRIGHT, Density of discriminants of cubic extensions, J. reine. angew. Math., 386 (1988), 116-138.
5. H. DAVENPORT, On a principle of Lipschitz, J. Lond. Math. Soc., 26 (1951), 179-183.
6. H. DAVENPORT, On the class number of binary cubic forms (I), J. Lond. Math. Soc., 26 (1951), 183-192 (erratum, ibid. 27 (1951), p. 512).
7. H. DAVENPORT, On the class number of binary cubic forms (II), J. Lond. Math. Soc., 26 (1951), 192-198.
8. H. DAVENPORT and H. HEILBRONN, On the density of discriminants of cubic fields (I), Bull. Lond. Math. Soc., 1 (1969), 345-348.
9. H. DAVENPORT and H. HEILBRONN, On the density of discriminants of cubic fields (II), Proc. Roy. Soc. Lond. A, 322 (1971), 405-420.
10. 3 + k, in Séminaire de Théorie des Nombres Paris, 1990-91, Birkhäuser, 1993, 61-83.
11. H. HALBERSTAM and H.E. RICHERT, Sieve methods, Academic Press, 1974.
12. H. HASSE, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Zeitschrift, 31 (1930), 565-582.
13. H. IWANIEC, A new form of the error term in the linear sieve, Acta. Arith., 37 (1980), 307-320.
14. H. IWANIEC, Rosser's sieve, Acta. Arith., 36 (1980), 171-202.
15. N.M. KATZ, Perversity and exponential sums, Adv. Stud. in Pure Math., 17 (1989), 210-259.
16. N.M. KATZ and G. LAUMON, Transformation de Fourier et majoration de sommes exponentielles, Pub. Math. IHES, 62 (1985), 361-418.
17. G.-B. MATHEWS, On the reduction and classification of binary cubic which have a negative discriminant, Proc. London Math. Soc., 10 (1912), 128-138.
18. J. QUER, Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12, C. R. Acad. Sciences, série I Math., 305 (1987), 215-218.
19. M. SATO and T. SHINTANI, On zeta functions associated with prehomogenous vector spaces, Ann. of Math., 100 (1974), 131-170.
20. T. SHINTANI, On Dirichlet series whose coefficients are class numbers of integral binary cubic forms, J. Math. Soc. Japan, 24 (1972), 132-188.
21. T. SHINTANI, On zeta-functions associated with the vector space of quadratic forms., J. Fac. Sci. Univ. Tokyo, Sec. Ia, 22 (1975), 25-66.
22. G. TENENBAUM, Introduction à la théorie analytique et probabiliste des nombres, Pub. Inst. Élie Cartan, 1990.
23. H. WEYL, On the volume of tubes, Amer. J. of Math., 61 (1939), 461-472.