Bounds for modular L-functions in the level aspect

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 40, Issue 5, 2007, Pages 697-740

  Blomer, Valentin ^a   Harcos, Gergely ^b   Michel, Philippe ^c  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38349130286     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ansens.2007.05.003     Document Type: Article

References (29)

1. Blomer V., Harcos G., Hybrid bounds for twisted L-functions, J. reine angew. Math., in press
2. Blomer V., Harcos G., and Michel P. A Burgess-like subconvex bound for twisted L-functions (with Appendix 2 by Z. Mao). Forum Math. 19 (2007) 61-105
3. Burgess D.A. On character sums and L-series. II. Proc. Lond. Math. Soc. 13 (1963) 524-536
4. Bykovskiǐ V.A. A trace formula for the scalar product of Hecke series and its applications. translated in. J. Math. Sci (New York) 89 (1998) 915-932
5. Deshouillers J.-M., and Iwaniec H. Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math. 70 (1982) 219-288
6. Duke W. Hyperbolic distribution problems and half-integral weight Maass forms. Invent. Math. 92 (1988) 73-90
7. Duke W., Friedlander J., and Iwaniec H. A quadratic divisor problem. Invent. Math. 115 (1994) 209-217
8. Duke W., Friedlander J., and Iwaniec H. Bounds for automorphic L-functions. II. Invent. Math. 115 (1994) 219-239
9. Duke W., Friedlander J., and Iwaniec H. Representations by the determinant and mean values of L-functions. Sieve Methods, Exponential Sums, and Their Applications in Number Theory. Cardiff, 1995. London Math. Soc. Lecture Note Ser. vol. 237 (1997), Cambridge Univ. Press, Cambridge 109-115
10. Duke W., Friedlander J., and Iwaniec H. Bounds for automorphic L-functions. III. Invent. Math. 143 (2001) 221-248
11. Duke W., Friedlander J., and Iwaniec H. The subconvexity problem for Artin L-functions. Invent. Math. 149 (2002) 489-577
12. Einsiedler M., Lindenstrauss E., Michel P., Venkatesh A., Distribution of periodic torus orbits and Duke's theorem for cubic fields, submitted for publication
13. Friedlander J. Bounds for L-functions. Zürich, 1994. Proc. Int. Congr. Math. vol. II (1995), Birkhäuser, Basel 363-373
14. 2 from the analytic point of view. In: Borel A., and Casselman W. (Eds). Automorphic Forms, Representations, and L-Functions, Part 1. Proc. Sympos. Pure Math. vol. 33 (1979) 213-251
15. Gradshteyn I.S., and Ryzhik I.M. Tables of Integrals, Series, and Products. fifth ed. (1994), Academic Press, New York
16. Harcos G. Uniform approximate functional equation for principal L-functions. Int. Math. Res. Not. (2002) 923-932 Erratum
17. Harcos G. Uniform approximate functional equation for principal L-functions. Int. Math. Res. Not. (2004) 659-660
18. Harcos G., and Michel P. The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. II. Invent. Math. 163 (2006) 581-655
19. Heath-Brown D.R. Hybrid bounds for Dirichlet L-functions. II. Quart. J. Math. Oxford Ser. (2) 31 (1980) 157-167
20. Iwaniec H., Spectral Methods of Automorphic Forms, second ed., Graduate Studies Mathematics, vol. 53, American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002
21. Iwaniec H., and Kowalski E. Analytic Number Theory. American Mathematical Society Colloquium Publications vol. 53 (2004), American Mathematical Society, Providence, RI
22. Iwaniec H., and Sarnak P. Perspectives in the analytic theory of L-functions. Geom. Funct. Anal. (2000) 705-741 Special Volume, Part II
23. Jutila M. Convolutions of Fourier coefficients of cusp forms. Publ. Inst. Math. (Beograd) (N.S.) 65 79 (1999) 31-51
24. 2 (with Appendix 1 by D. Ramakrishnan and Appendix 2 by H. Kim and P. Sarnak). J. Amer. Math. Soc. 16 (2003) 139-183
25. Kowalski E., Michel P., and VanderKam J. Mollification of the fourth moment of automorphic L-functions and arithmetic applications. Invent. Math. 142 (2000) 95-151
26. Meurman T. On the binary additive divisor problem. Number Theory. Turku, 1999 (2001), de Gruyter, Berlin 223-246
27. Michel P. The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. Ann. of Math. 160 (2004) 185-236
28. Michel P., and Venkatesh A. Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik. Madrid, 2006. Proc. Int. Congr. Math. vol. II (2006), Eur. Math. Soc., Zürich 421-457
29. Proskurin N.V. On the general Kloosterman sums, translated in. J. Math. Sci. (New York) 129 (2005) 3874-3889