Comptes Rendus
no. 1-2
Number Theory
On certain exponential sums related to GL(3) cusp forms
[Sur les sommes exponentielles associées aux GL(3)-formes cuspidales]

Présenté par : Gérard Laumon

Anne-Maria Ernvall-Hytönen1
1 Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden
Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 5-8.

We will prove a sharp estimate for certain exponential sums of Fourier coefficients of GL(3) cusp forms.

On montre une estimation precise pour quelques sommes exponentielles des coefficients de Fourier des GL(3)-formes cuspidales.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.012

Anne-Maria Ernvall-Hytönen 1

1 Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden 
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Anne-Maria Ernvall-Hytönen. On certain exponential sums related to $ \mathrm{GL}(3)$ cusp forms. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 5-8. doi : 10.1016/j.crma.2009.12.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.012/

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  • Huan Qin; Yang Bo Ye Bounds for average toward the resonance barrier for \mathrm{GL}(3) {{\times}}{{\mathrm}}{GL}(2) automorphic forms, Acta Mathematica Sinica. English Series, Volume 39 (2023) no. 9, pp. 1667-1683 | DOI:10.1007/s10114-023-1022-4 | Zbl:1548.11078
  • Timothy Gillespie; Praneel Samanta; Yangbo Ye Double square moments and bounds for resonance sums of cusp forms, Journal of Number Theory, Volume 246 (2023), pp. 166-188 | DOI:10.1016/j.jnt.2022.11.012 | Zbl:1512.11040
  • Yangbo Ye Bounds toward hypothesis S for cusp forms, Journal of Number Theory, Volume 236 (2022), pp. 128-143 | DOI:10.1016/j.jnt.2021.07.012 | Zbl:1498.11119
  • Jesse Jääsaari; Esa V. Vesalainen Exponential sums related to Maass forms, Acta Arithmetica, Volume 190 (2019) no. 1, pp. 1-48 | DOI:10.4064/aa8447-9-2018 | Zbl:1460.11108
  • Nathan Salazar; Yangbo Ye Spectral square moments of a resonance sum for Maass forms, Frontiers of Mathematics in China, Volume 12 (2017) no. 5, pp. 1183-1200 | DOI:10.1007/s11464-016-0621-0 | Zbl:1430.11077
  • Kyle Czarnecki Resonance sums for Rankin-Selberg products of SLm(Z) Maass cusp forms, Journal of Number Theory, Volume 163 (2016), pp. 359-374 | DOI:10.1016/j.jnt.2015.11.003 | Zbl:1408.11044
  • Xiumin Ren; Yangbo Ye Hyper-Kloosterman Sums of Different Moduli and Their Applications to Automorphic Forms for SLm(Z), Taiwanese Journal of Mathematics, Volume 20 (2016) no. 6 | DOI:10.11650/tjm.20.2016.7389
  • Fei Hou; Yujiao Jiang; Guangshi Lü ON EXPONENTIAL SUMS INVOLVING COEFFICIENTS OFL-FUNCTIONS FOR SL(3, ℤ) OVER PRIMES, The Quarterly Journal of Mathematics, Volume 67 (2016) no. 2, p. 285 | DOI:10.1093/qmath/haw006
  • Anne-Maria Ernvall-Hytönen; Jesse Jääsaari; Esa V. Vesalainen Resonances and Ω-results for exponential sums related to Maass forms for \mathrm{SL}(n, {{\mathbb}}{Z}), Journal of Number Theory, Volume 153 (2015), pp. 135-157 | DOI:10.1016/j.jnt.2015.01.014 | Zbl:1357.11067

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