Revêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères

Journal of Number Theory

Volumn 64, Issue 2, 1997, Pages 165-182

  Leprevost F ^a   Morain, F ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b ÉCOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031164785     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.1997.2070     Document Type: Article

References (29)

1. Atkin A. O. L., Morain F. Elliptic curves and primality proving. Math. Comp. 61:Juil. 1993;29-67.
2. Batut C., Bernardi D., Cohen H., Olivier M. User's Guide to PARI-GP. 1990;Université de Bordeaux I.
3. Berndt B. C., Evans R. J. Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer. Illinois J. Math. 23:1979;374-437.
4. Berndt B. C., Evans R. J. Sums of Gauss, Jacobi, and Jacobsthal. J. Number Theory. 11:1979;349-398.
5. Bolza O. On binary sextics with linear transformations onto themselves. Amer. J. Math. 10:1888;47-70.
6. Borel A., Chowla S., Herz C. S., Iwasawa K., Serre J. P. Seminar on complex multiplication. Lecture Notes in Math. 21:1966;Springer-Verlag, New York/Berlin.
7. Brewer B. W. On certain character sums. Trans. Amer. Math. Soc. 99:1961;241-245.
8. 2. Proc. Amer. Math. Soc. 17:1966;502-509.
9. J.-M. Couveignes, A. Joux, F. Morain, Fev. 1994, Sur quelques sommes de caractères.
10. 2. 1989;Wiley, New York.
11. Deuring M. Die Klassenkörper der komplexen Multiplikation. Enzyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. 1958;Teubner, Stuttgart.
12. Giudici R. E., Muskat J. B., Robinson S. F. On the evaluation of Brewer's character sums. Trans. Amer. Math. Soc. 171:Sept. 1972;317-347.
13. Hudson R. H., Williams K. S. An application of a formula of Western to the evaluation of certain Jacobsthal sums. Acta Arithmetica. 41:1982;261-276.
14. Hudson R. H., Williams K. S. Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums. Pacific J. Math. 99:1982;379-386.
15. Ireland K., Rosen M. A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics. 84:1982;Springer-Verlag, New York/Berlin.
16. Joux A., Morain F. Sur les sommes de caractères liées aux courbes elliptiques à multiplication complexe. J. Number Theory. 55:Nov. 1995;108-128.
17. 2p. Pacific J. Math. 5:1955;103-118.
18. Lehmer E. Criteria for cubic and quartic residuacity. Mathematika. 5:1958;20-29.
19. Lidl R., Mullen G. L., Turnwald G. Dickson Polynomials. Pitman Monographs and Surveys in Pure and Applied Mathematics. 65:1993;Longman Scientific.
20. Monzingo M. G. An elementary evaluation of the Jacobsthal sum. J. Number Theory. 22:1986;21-25.
21. Rajwade A. R. Arithmetic on curves with complex multiplication by √-2 . Proc. Cambridge Philos. Soc. 64:1968;659-672.
22. Rajwade A. R. Certain classical congruences via elliptic curves. J. London Math. Soc. 2:1974;60-62.
23. 2. J. Australian Math. Soc. Ser. A. 24:1977;286-295.
24. Robinson S. F. Theorems on Brewer sums. Pacific J. Math. 25:1968;587-596.
25. Ruppert W. M. When is an abelian surface isomorphic or isogeneous to a product of elliptic curves? Math. Z. 203:1990;293-299.
26. 3. J. Reine Angew. Math. 286/287:1976;46-74.
27. Shioda T., Mitani N. Singular abelian surfaces and binary quadratic forms. Popp H. Classification of Algebraic Varieties and Compact Complex Manifolds. Lecture Notes in Math. 412:1974;259-287 Springer-Verlag, New York/Berlin.
28. Weber H. Lehrbuch der Algebra. 1902;Chelsea Publishing, New York.
29. Yui N., Zagier D. On the Singular Values of Weber Modular Functions. 1994;Max Planck Institüt.