A larger GL 2 large sieve in the level aspect
Open Mathematics (2012)
- Volume: 10, Issue: 2, page 748-760
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
topGoran Djanković. "A larger GL 2 large sieve in the level aspect." Open Mathematics 10.2 (2012): 748-760. <http://eudml.org/doc/269440>.
@article{GoranDjanković2012,
abstract = {In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.},
author = {Goran Djanković},
journal = {Open Mathematics},
keywords = {Orthogonality; Large sieve; Hecke eigenvalues; Holomorphic cusp forms; orthogonality; large sieve; holomorphic cusp forms},
language = {eng},
number = {2},
pages = {748-760},
title = {A larger GL 2 large sieve in the level aspect},
url = {http://eudml.org/doc/269440},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Goran Djanković
TI - A larger GL 2 large sieve in the level aspect
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 748
EP - 760
AB - In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
LA - eng
KW - Orthogonality; Large sieve; Hecke eigenvalues; Holomorphic cusp forms; orthogonality; large sieve; holomorphic cusp forms
UR - http://eudml.org/doc/269440
ER -
References
top- [1] Bombieri E., Friedlander J.B., Iwaniec H., Primes in arithmetic progressions to large moduli, Acta Math., 1986, 156(3–4), 203–251 http://dx.doi.org/10.1007/BF02399204 Zbl0588.10042
- [2] Conrey J.B., Iwaniec H., Soundararajan K., Asymptotic large sieve, preprint available at http://arxiv.org/abs/1105.1176
- [3] Deshouillers J.-M., Iwaniec H., Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math., 1982, 70(2), 219–288 http://dx.doi.org/10.1007/BF01390728 Zbl0502.10021
- [4] Iwaniec H., Topics in Classical Automorphic Forms, Grad. Stud. Math., 17, American Mathematical Society, Providence, 1997 Zbl0905.11023
- [5] Iwaniec H., Kowalski E., Analytic Number Theory, Amer. Math. Soc. Colloq. Publ., 53, American Mathematical Society, Providence, 2004 Zbl1059.11001
- [6] Iwaniec H., Li X., The orthogonality of Hecke eigenvalues, Compos. Math., 2007, 143(3), 541–565 Zbl1149.11023
- [7] Iwaniec H., Sarnak P., Perspectives on the analytic theory of L-functions, Geom. Funct. Anal., 2000, Special Volume, Part II, 705–741 Zbl0996.11036
- [8] Oberhettinger F., Tables of Bessel Transforms, Springer, New York-Heidelberg, 1972 http://dx.doi.org/10.1007/978-3-642-65462-6 Zbl0261.65003
- [9] Watson G.N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944 Zbl0063.08184
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.