Character sums in complex half-planes
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 χG ^ such that aA 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 χG ^ tel que aA χ(a)P.

Published online:
DOI: 10.5802/jtnb.463
Sergei V. Konyagin 1; Vsevolod F. Lev 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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Sergei V. Konyagin; Vsevolod F. Lev. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.463/

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