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Character sums in complex half-planes

Sergei V. Konyagin, Vsevolod F. Lev (2004)

Journal de Théorie des Nombres de Bordeaux

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 .

Computing higher rank primitive root densities

P. Moree, P. Stevenhagen (2014)

Acta Arithmetica

We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...

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