Nous démontrons une inégalité du type grand crible pour les formes de Maass et les formes cuspidales holomorphes de niveau au moins un et de poids entier ou demi-entier dans un petit intervalle.
We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.
@article{JTNB_2014__26_3_757_0,
author = {Lam, Jonathan Wing Chung},
title = {A local large sieve inequality for cusp forms},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {757--787},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {26},
number = {3},
year = {2014},
doi = {10.5802/jtnb.887},
mrnumber = {3320500},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.887/}
}
TY - JOUR AU - Lam, Jonathan Wing Chung TI - A local large sieve inequality for cusp forms JO - Journal de théorie des nombres de Bordeaux PY - 2014 SP - 757 EP - 787 VL - 26 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.887/ DO - 10.5802/jtnb.887 LA - en ID - JTNB_2014__26_3_757_0 ER -
%0 Journal Article %A Lam, Jonathan Wing Chung %T A local large sieve inequality for cusp forms %J Journal de théorie des nombres de Bordeaux %D 2014 %P 757-787 %V 26 %N 3 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.887/ %R 10.5802/jtnb.887 %G en %F JTNB_2014__26_3_757_0
Lam, Jonathan Wing Chung. A local large sieve inequality for cusp forms. Journal de théorie des nombres de Bordeaux, Tome 26 (2014) no. 3, pp. 757-787. doi : 10.5802/jtnb.887. http://www.numdam.org/articles/10.5802/jtnb.887/
[1] J. Cogdell and P. Michel, On the complex moments of symmetric power L-functions at s=1 , Int. Math. Res. Not. 31 , (2004), 1561–1617. | MR | Zbl
[2] J.M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier cofficients of cusp forms, Invent. Math. 70, (1982), 219–288. | MR | Zbl
[3] W. Duke, J.B. Frielander and H. Iwaniec, Bounds for Automorphic L-functions II, Invent. Math. 115, (1994), 219–239. | MR | Zbl
[4] H. Iwaniec, Mean values for Fourier coefficients of cusp forms and sums of Kloosterman sums, Journées Arithmetiqués de Exeter, (1980), 306–321. | MR | Zbl
[5] H. Iwaniec, Spectral Methods of Automorphic Forms, Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI, (2002). | MR | Zbl
[6] H. Iwaniec and P. Michel, The second moment of the symmetric square L-functions, Ann. Acad. Sci. Fenn. Math. 2, (2001), 465–482. | MR | Zbl
[7] H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematics Society Colloquium Publications, Amer. Math. Soc., Providence, RI, (2004). | MR | Zbl
[8] H. Iwaniec, W. Luo and P. Sarnak, P., Low lying zeros of families of L-functions, I.H.E.S. Publ. Math., 91, (2000), 55–131. | MR | Zbl
[9] M. Jutila, On spectral large sieve inequalities, Functiones et Approximatio 28, (2000), 7–18. | MR | Zbl
[10] M. Jutila and Y. Motohashi, Uniform bound for Hecke L-functions, Acta. Math.195, (2005), 61–115. | MR | Zbl
[11] N.N. Lebedev, Special functions and their applications, Dover Books on Mathematics, (1972). | MR | Zbl
[12] W. Luo, Spectral means-values of automorphic L-functions at special points, Analytic Number Theory, Proc. of a Conference in honor of Heini Halberstam, 70, (1982), 219–288. | Zbl
[13] W. Luo and P. Sarnak, Mass equidistribution for Hecke eigenforms, Comm. Pure Appl. Math., 56, (2003), 874–891. | MR | Zbl
[14] Y. Motohashi, Spectral Theory of the Riemann Zeta-Function, Merchant Books, (2008). | Zbl
[15] H.E. Richert, Lectures on Sieve Methods, Tata Institute of Fundamental Research, Bombay, (1976). | Zbl
[16] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, 127, (1997). | MR | Zbl
[17] Q. Zhang, A local large sieve inequality for the Maass cusp form. preprint.
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