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Sergei V. Konyagin; Vsevolod F. Lev
Character sums in complex half-planes
Journal de théorie des nombres de Bordeaux, 16 no. 3 (2004), p. 587-606, doi: 10.5802/jtnb.463
Article PDF | Reviews MR 2144960 | Zbl 1068.43004

Résumé - 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 $\sum _{a\in A} \chi (a)\in P$.

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