Bounds for modular L-functions in the level aspect
Blomer, Valentin1 ; Harcos, Gergely ; Michel, Philippe2
1 University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)
2 Université Montpellier II, Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex (France)
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 5, pp. 697-740.
DOI : 10.1016/j.ansens.2007.05.003
Blomer, Valentin 1 ; Harcos, Gergely  ; Michel, Philippe 2

1 University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)
2 Université Montpellier II, Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex (France) 
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Blomer, Valentin; Harcos, Gergely; Michel, Philippe. Bounds for modular $L$-functions in the level aspect. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 5, pp. 697-740. doi : 10.1016/j.ansens.2007.05.003. http://www.numdam.org/articles/10.1016/j.ansens.2007.05.003/

[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

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

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

[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

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

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