Comptes Rendus
Number Theory
On certain exponential sums related to GL(3) cusp forms
[Sur les sommes exponentielles associées aux GL(3)-formes cuspidales]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 5-8.

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

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

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/

[1] A.-M. Ernvall-Hytönen; K. Karppinen On short exponential sums involving Fourier coefficients of holomorphic cusp forms, Int. Math. Res. Not., Volume 2008 (2008) (Art. ID rnn022, 44 pp)

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[5] X. Li The central value of the Rankin–Selberg L-functions | arXiv

[6] S.D. Miller Cancellation in additively twisted sums on GL(n), Amer. J. Math., Volume 128 (2006) no. 3, pp. 699-729

[7] S.D. Miller; W. Schmid Automorphic distributions, L-functions, and Voronoi summation for GL(3), Ann. of Math. (2), Volume 164 (2006) no. 2, pp. 423-488

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