Bounding hyperbolic and spherical coefficients of Maass forms

Valentin Blomer[1]; Farrell Brumley[2]; Alex Kontorovich[3]; Nicolas Templier[4]

  • [1] Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen, Germany
  • [2] Institut Galilée, Université Paris 13 99 avenue J.-B. Clément 93430 Villetaneuse, France
  • [3] Department of Mathematics Yale University New Haven, CT 06511 USA
  • [4] Department of Mathematics Fine Hall, Washington Road Princeton, NJ 08544 USA

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 3, page 559-578
  • ISSN: 1246-7405

Abstract

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We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.

How to cite

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Blomer, Valentin, et al. "Bounding hyperbolic and spherical coefficients of Maass forms." Journal de Théorie des Nombres de Bordeaux 26.3 (2014): 559-578. <http://eudml.org/doc/275819>.

@article{Blomer2014,
abstract = {We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.},
affiliation = {Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen, Germany; Institut Galilée, Université Paris 13 99 avenue J.-B. Clément 93430 Villetaneuse, France; Department of Mathematics Yale University New Haven, CT 06511 USA; Department of Mathematics Fine Hall, Washington Road Princeton, NJ 08544 USA},
author = {Blomer, Valentin, Brumley, Farrell, Kontorovich, Alex, Templier, Nicolas},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Maass forms; Fourier coefficients; geodesics; periods; equidistribution; Sobolev norms; wave front lemma},
language = {eng},
month = {12},
number = {3},
pages = {559-578},
publisher = {Société Arithmétique de Bordeaux},
title = {Bounding hyperbolic and spherical coefficients of Maass forms},
url = {http://eudml.org/doc/275819},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Blomer, Valentin
AU - Brumley, Farrell
AU - Kontorovich, Alex
AU - Templier, Nicolas
TI - Bounding hyperbolic and spherical coefficients of Maass forms
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/12//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 3
SP - 559
EP - 578
AB - We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.
LA - eng
KW - Maass forms; Fourier coefficients; geodesics; periods; equidistribution; Sobolev norms; wave front lemma
UR - http://eudml.org/doc/275819
ER -

References

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  10. A. Reznikov, Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms. J. Amer. Math. Soc. 21, (2008), no. 2, 439–477. Zbl1188.11024MR2373356
  11. A. Reznikov, Geodesic restrictions for the Casimir operator. J. Funct. Anal. 261, (2011), no. 9, 2437–2460. Zbl1229.53048MR2826400
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