Bounds for modular L-functions in the level aspect
Blomer, Valentin ; Harcos, Gergely ; Michel, Philippe
Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007), p. 697-740 / Harvested from Numdam
@article{ASENS_2007_4_40_5_697_0,
     author = {Blomer, Valentin and Harcos, Gergely and Michel, Philippe},
     title = {Bounds for modular $L$-functions in the level aspect},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {40},
     year = {2007},
     pages = {697-740},
     doi = {10.1016/j.ansens.2007.05.003},
     zbl = {pre05240226},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_5_697_0}
}
Blomer, Valentin; Harcos, Gergely; Michel, Philippe. Bounds for modular $L$-functions in the level aspect. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 697-740. doi : 10.1016/j.ansens.2007.05.003. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_5_697_0/

[1] Blomer V., Harcos G., Hybrid bounds for twisted L-functions, J. reine angew. Math., in press.

[2] Blomer V., Harcos G., Michel P., A Burgess-like subconvex bound for twisted L-functions (with Appendix 2 by Z. Mao), Forum Math. 19 (2007) 61-105. | MR 2296066 | Zbl pre05145751

[3] Burgess D.A., On character sums and L-series. II, Proc. Lond. Math. Soc. 13 (1963) 524-536. | MR 148626 | Zbl 0123.04404

[4] Bykovskiĭ 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. | MR 1433344 | Zbl 0898.11017

[5] Deshouillers J.-M., Iwaniec H., Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982) 219-288. | MR 684172 | Zbl 0502.10021

[6] Duke W., Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988) 73-90. | MR 931205 | Zbl 0628.10029

[7] Duke W., Friedlander J., Iwaniec H., A quadratic divisor problem, Invent. Math. 115 (1994) 209-217. | MR 1258903 | Zbl 0791.11049

[8] Duke W., Friedlander J., Iwaniec H., Bounds for automorphic L-functions. II, Invent. Math. 115 (1994) 219-239. | MR 1258904 | Zbl 0812.11032

[9] Duke W., Friedlander J., Iwaniec H., Representations by the determinant and mean values of L-functions, in: Sieve Methods, Exponential Sums, and Their Applications in Number Theory, Cardiff, 1995, London Math. Soc. Lecture Note Ser., vol. 237, Cambridge Univ. Press, Cambridge, 1997, pp. 109-115. | MR 1635738 | Zbl 0927.11046

[10] Duke W., Friedlander J., Iwaniec H., Bounds for automorphic L-functions. III, Invent. Math. 143 (2001) 221-248. | MR 1835388 | Zbl 1163.11325

[11] Duke W., Friedlander J., Iwaniec H., The subconvexity problem for Artin L-functions, Invent. Math. 149 (2002) 489-577. | MR 1923476 | Zbl 1056.11072

[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, in: Zürich, 1994, Proc. Int. Congr. Math., vol. II, Birkhäuser, Basel, 1995, pp. 363-373. | MR 1403937 | Zbl 0843.11040

[14] Gelbart S., Jacquet H., Forms on GL 2 from the analytic point of view, in: Borel A., Casselman W. (Eds.), Automorphic Forms, Representations, and L-Functions, Part 1, Proc. Sympos. Pure Math., vol. 33, 1979, pp. 213-251. | MR 546600 | Zbl 0409.22013

[15] Gradshteyn I.S., Ryzhik I.M., Tables of Integrals, Series, and Products, fifth ed., Academic Press, New York, 1994. | Zbl 0918.65002

[16] Harcos G., Uniform approximate functional equation for principal L-functions, Int. Math. Res. Not. (2002) 923-932, Erratum, Int. Math. Res. Not. (2004) 659-660. | MR 1902296 | Zbl 0998.11026

[17] Harcos G., Michel P., The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points. II, Invent. Math. 163 (2006) 581-655.

[18] Heath-Brown D.R., Hybrid bounds for Dirichlet L-functions. II, Quart. J. Math. Oxford Ser. (2) 31 (1980) 157-167. | MR 576334 | Zbl 0396.10030

[19] Iwaniec H., Spectral Methods of Automorphic Forms, second ed., Graduate Studies Mathematics, vol. 53, American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. | MR 1942691 | Zbl 1006.11024

[20] Iwaniec H., Kowalski E., Analytic Number Theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. | MR 2061214 | Zbl 1059.11001

[21] Iwaniec H., Sarnak P., Perspectives in the analytic theory of L-functions, Geom. Funct. Anal. (2000) 705-741, Special Volume, Part II. | MR 1826269 | Zbl 0996.11036

[22] Jutila M., Convolutions of Fourier coefficients of cusp forms, Publ. Inst. Math. (Beograd) (N.S.) 65 (79) (1999) 31-51. | MR 1717400 | Zbl 1006.11019

[23] Kim H., Functoriality for the exterior square of GL 4 and the symmetric fourth of GL 2 (with Appendix 1 by D. Ramakrishnan and Appendix 2 by H. Kim and P. Sarnak), J. Amer. Math. Soc. 16 (2003) 139-183. | MR 1937203 | Zbl 1018.11024

[24] Kowalski E., Michel P., Vanderkam J., Mollification of the fourth moment of automorphic L-functions and arithmetic applications, Invent. Math. 142 (2000) 95-151. | MR 1784797 | Zbl 1054.11026

[25] Meurman T., On the binary additive divisor problem, in: Number Theory, Turku, 1999, de Gruyter, Berlin, 2001, pp. 223-246. | MR 1822012 | Zbl 0967.11039

[26] Michel P., The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points, Ann. of Math. 160 (2004) 185-236.

[27] Michel P., Venkatesh A., Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik, in: Madrid, 2006, Proc. Int. Congr. Math., vol. II, Eur. Math. Soc., Zürich, 2006, pp. 421-457. | MR 2275604 | Zbl pre05057405

[28] Proskurin N.V., On the general Kloosterman sums, translated in, J. Math. Sci. (New York) 129 (2005) 3874-3889. | MR 2023036 | Zbl 1140.11340