A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations

Inventiones Mathematicae

Volumn 139, Issue 1, 2000, Pages 1-39

  Duke, W ^a   Kowalski, E ^b  

^a RUTGERS UNIVERSITY   (United States)

^b Fine Hall ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034358461     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002229900017     Document Type: Article

References (25)

1. Bushnell, C.J., Henniart, G.: An upper bound on conductors for pairs, J. Number Theory 65(2), 183-196 (1997)
2. Brumer, A., Silverman, J.: The number of elliptic curves over Q with conductor N, Manuscripta Math. 91, 95-102 (1996)
3. Davenport, H., Heilbronn, H.: On the density of discriminants of cubic fields. II, Proc. Royal Soc., A 322, 405-420 (1971 ) or Collected Works of Harold Davenport, vol. 2, 535-550, Academic Press (1977)
4. Deligne, P.: Formes modulaires et représentations de GL(2), Modular Forms in One Variable IV, Springer Lecture Notes 749, 55-105 (1972)
5. Duke, W., Friedlander, J., Iwaniec, H.: Bounds for automorphic L-functions, II, Invent. Math. 115, 219-239 (1994)
6. Deshouillers, J.M., Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70, 219-288 (1983)
7. Fouvry, É., Nair, M., Tenenbaum, G.: L'ensemble exceptionnel dans la conjecture de Szpiro, Bull. Soc. Math. France 120(4), 483-506 (1992)
8. Gelbart, S.: Automorphic forms on adele groups, Princeton University Press (1975)
9. Gelbart, S., Jacquet, H.: A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. E.N.S 4ème série 11, 471-552 (1978)
10. Hoffstein, J., Lockhart, P.: Coefficients of Maass forms and the Siegel zero (with an appendix by D. Goldfeld, J. Hoffstein and D. Lieman), Ann. of Math. (2) 140, 161-181 (1994)
11. Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers, Fifth Edition, Oxford University Press (1979)
12. Iwaniec, H.: Introduction to the Spectral Theory of Automorphic Forms, Biblioteca de la Revista Matemática Iberoamericana (1995)
13. Jacquet, H., Piatetskii-Shapiro, I. I., Shalika, J. A.: Rankin-Selberg convolutions, Amer. J. Math. 105, 367-464 (1983)
14. Linnik, Yu. V: The Large Sieve, Dokl. Akad. Nauk. SSSR 30, 292-294 (1941), in Russian
15. Luo, W., Rudnick, Z., Sarnak, P.: On Selberg's eigenvalue conjecture, Geom. Funct. Anal. 5, 387-401 (1995)
16. Luo, W.: Values of symmetric square L-functions at I, J. Reine Angew. Math. 506, 215-235 (1999)
17. Miyake, T.: Elliptic Modular Forms. Springer-Verlag (1990)
18. Montgomery, H.L.: Topics in Multiplicative Number Theory, Lect. Notes Math. 227, Springer-Verlag (1971)
19. Moeglin, C., Waldspurger, J.L.: Pôles des fonctions L de paires pour GL(N), appendice to Le spectre résiduel de GL(n), Ann. Sci. ENS (4ème série) 22, 605-674 (1989)
20. Rudnick, Z., Sarnak, P.: Zeros of principal L-functions and random matrix theory. A celebration of John F. Nash, Jr., Duke Math. J. 81(2), 269-322 (1996)
21. Serre, J.-P.: Quelques applications du théorème de densité de Chebotarev, Pub. Math. I.H.E.S 54, 123-201 (1981)
22. Shimura, G.: Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press (1971)
23. Silverman, J.: The arithmetic of elliptic curves, Grad. Texts in Math. 106, Springer Verlag (1986)
24. Silverman, J.: Advanced topics in the arithmetic of elliptic curves, Grad. Texts in Math. 151, Springer Verlag (1994)
25. Wiles, A.: Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141, 443-551 (1995)