Character sums in complex half-planes

Konyagin, Sergei V., and Lev, Vsevolod F.. "Character sums in complex half-planes." Journal de Théorie des Nombres de Bordeaux 16.3 (2004): 587-606. <http://eudml.org/doc/249259>.

@article{Konyagin2004,
abstract = {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 $\chi \in \{\widehat\{G\}\}$ such that $\sum _\{a\in A\} \chi (a)\in P$.},
affiliation = {Department of Mechanics and Mathematics Moscow State University Moscow, Russia; Department of Mathematics Haifa University at Oranim Tivon 36006, Israel},
author = {Konyagin, Sergei V., Lev, Vsevolod F.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {character group; Fourier coefficients; character sums},
language = {eng},
number = {3},
pages = {587-606},
publisher = {Université Bordeaux 1},
title = {Character sums in complex half-planes},
url = {http://eudml.org/doc/249259},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Konyagin, Sergei V.
AU - Lev, Vsevolod F.
TI - Character sums in complex half-planes
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 3
SP - 587
EP - 606
AB - 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 $\chi \in {\widehat{G}}$ such that $\sum _{a\in A} \chi (a)\in P$.
LA - eng
KW - character group; Fourier coefficients; character sums
UR - http://eudml.org/doc/249259
ER -