Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique

Revista Matematica Iberoamericana

Volumn 21, Issue 1, 2005, Pages 263-312

  Royer, Emmanuel ^a,b   Wu, Jie ^c  

^a UNIVERSITÉ DE MONTPELLIER   (France)

^b UNIVERSITÉ PAUL VALÉRY   (France)

^c UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Carr sym trique; Fonction L; Forme automorphe; Valeur sp ciale

Indexed keywords

EID: 21344435050     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/423     Document Type: Article

References (24)

1. AKBARY, A.: Average values of symmetric square L-functions at Re(s) = 2. C. R. Math. Acad. Sci. Soc. R. Can. 22 (2000), no. 3, 97-104.
2. DUKE, W. AND KOWALSKI, E.: A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations. Invent. Math. 139 (2000), no. 1, 1-39.
3. DUKE, W.: Extreme values of Artin L-functions and class numbers. Compositio Math. 136 (2003), no. 1, 103-115.
4. FREY, G.: On ternary equations of Fermat type and relations with elliptic curves. In Modular forms and Fermat's fast theorem (Boston, MA, 1995), 527-548. Springer, New York, 1997.
5. GOLDFELD, D., HOFFSTEIN, J. AND LIEMAN, D.: An effective zero-free region. Ann. of Math. (2) 140 (1994), no. 1, 177-181, appendice de [7].
6. HABSIEGER, L. AND ROYER, E.: Interprétation combinatoire des moments positifs des valeurs de fonctions L au bord de la bande critique. À paraître dans Ann. Inst. Fourier (Grenoble).
7. HOFFSTEIN, J. AND LOCKHART, P.: Coefficients of Maass forms and the Siegel zero. Ann. of Math. (2) 140 (1994), no. 1, 161-181.
8. IWANIEC, H., LUO, W. AND SARNAK, P.: Low lying zeros of families of L-functions. Inst. Hautes Études Sci. Publ. Math. No. 91 (2000), 55-131 (2001).
9. IWANIEC, H. AND MICHEL, P.: The second moment of the symmetric square L-functions. Ann. Acad. Sci. Fenn. Math. 26 (2001), 465-482.
10. IWANIEC, H.: Topics in classical automorphic forms. Graduate Studies in Mathematics 17. American Mathematical Society, Providence, Rhode Island, 1997.
11. 0(q) and zeros of automorphic L-functions. Duke Math. J. 100 (1999), no. 3, 503-542.
12. KOWALSKI, E. AND MICHEL, P.: Zeros of families of automorphic L-functions close to 1. Pacific J. Math. 207 (2002), no. 2, 411-431.
13. LAU, Y.-K.: On the error term in an asymptotic formula for symmetric square L-function. Proc. Amer. Math. Soc. 132 (2004), no. 2, 317-323.
14. Luo, W.: Values of symmetric square L-functions at 1. J. Reine Angew. Math. 506 (1999), 215-235.
15. Luo, W.: Nonvanishing of L-values and the Weyl law. Ann. of Math. (2) 154 (2001), no. 2, 477-502.
16. MICHEL, P.: Analytic number theory and families of automorphic L-functions. Lectures from the Graduate Summer School held in Park City, Summer 2002, IAS/Park City Mathematics Series, American Mathematical Society, Providence, RI, à paraître.
17. 0(N)(Q). In Number theory (Halifax, NS, 1994), 263-277. CMS Conf. Proc. 15. Amer. Math. Soc., Providence, RI, 1995
18. 2f, 1). Math. Ann. 321 (2001), no. 3, 667-687.
19. ROYER, E.: Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique. Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 4, 601-620.
20. SERRE, J.-P.: Cours d'arithmétique. Deuxième édition revue et corrigée. Le Mathématicien, No. 2. Presses Universitaires de France, Paris, 1977.
21. TITCHMARSH, E. G.: The theory of functions, seconde éd. Oxford University Press, Oxford, 1952.
22. TITCHMARSH, E. C.: The theory of the Riemann zeta-function, seconde éd. The Clarendon Press, Oxford University Press, New York, 1986.
23. WU, J.: Average values of symmetric square L-functions at the edge of the critical strip. Proc. Amer. Math. Soc. 131 (2003), no. 4, 1063-1070.
24. ZAGIER, D.: Modular parametrizations of elliptic curves. Canad. Math. Bull. 28 (1985), no. 3, 372-384.