no. 3
Character sums in complex half-planes
Konyagin, Sergei V.1; Lev, Vsevolod F.2
1 Department of Mechanics and Mathematics Moscow State University Moscow, Russia
2 Department of Mathematics Haifa University at Oranim Tivon 36006, Israel
Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 587-606.

Let A be a finite subset of an abelian group G and let P be a closed half-plane of the complex plane, containing zero. We show that (unless A possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of A which belongs to P. In other words, there exists a non-trivial character χ∈G ^ such that ∑ a∈A χ(a)∈P.

Soit A un sous-ensemble fini d’un groupe abélien G et P un demi-plan fermé du plan complexe contenant zéro. Nous montrons qu’il existe un coefficient de Fourier non-trivial de la fonction indicatrice de A qui appartient à P (si A ne possède pas une structure spéciale explicite). Autrement dit, il existe un caractère non-trivial χ∈G ^ tel que ∑ a∈A χ(a)∈P.

DOI: 10.5802/jtnb.463
Konyagin, Sergei V. 1; Lev, Vsevolod F. 2

1 Department of Mechanics and Mathematics Moscow State University Moscow, Russia
2 Department of Mathematics Haifa University at Oranim Tivon 36006, Israel 
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Konyagin, Sergei V.; Lev, Vsevolod F. Character sums in complex half-planes. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 587-606. doi : 10.5802/jtnb.463. http://archive.numdam.org/articles/10.5802/jtnb.463/

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