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
Ernvall-Hytönen, Anne-Maria1
1 Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden
Comptes Rendus. Mathématique, Tome 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

Ernvall-Hytönen, Anne-Maria 1

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

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

[2] Goldfeld, D.; Li, X. Voronoi formulas on GL(n), Int. Math. Res. Not. (2006) (Art. ID 86295, 25 pp)

[3] Jutila, M. On exponential sums involving the Ramanujan function, Proc. Indian Acad. Sci. Math. Sci., Volume 97 (1987) no. 1–3, pp. 157-166

[4] Jutila, M.; Motohashi, Y. Uniform bound for Hecke L-functions, Acta Math., Volume 195 (2005), pp. 61-115

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

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

[7] Miller, S.D.; Schmid, W. 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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