Comptes Rendus
no. 1-2
Number Theory
On certain exponential sums related to GL(3) cusp forms
Gérard Laumon
Anne-Maria Ernvall-Hytönen1
1Department 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.

Received:
Accepted:
Published online:
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 
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
@article{CRMATH_2010__348_1-2_5_0,
     author = {Anne-Maria Ernvall-Hyt\"onen},
     title = {On certain exponential sums related to $ \mathrm{GL}(3)$ cusp forms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {5--8},
     year = {2010},
     publisher = {Elsevier},
     volume = {348},
     number = {1-2},
     doi = {10.1016/j.crma.2009.12.012},
     language = {en},
}
TY  - JOUR
AU  - Anne-Maria Ernvall-Hytönen
TI  - On certain exponential sums related to $ \mathrm{GL}(3)$ cusp forms
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 5
EP  - 8
VL  - 348
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crma.2009.12.012
LA  - en
ID  - CRMATH_2010__348_1-2_5_0
ER  - 
%0 Journal Article
%A Anne-Maria Ernvall-Hytönen
%T On certain exponential sums related to $ \mathrm{GL}(3)$ cusp forms
%J Comptes Rendus. Mathématique
%D 2010
%P 5-8
%V 348
%N 1-2
%I Elsevier
%R 10.1016/j.crma.2009.12.012
%G en
%F CRMATH_2010__348_1-2_5_0

[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)

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

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

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

[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

Cited by Sources:

Comments - Policy