Archiv der Mathematik

, Volume 96, Issue 5, pp 417–421 | Cite as

On twisted character sums



In this paper we give a simple proof of a result by Burgess about short sums involving Dirichlet characters and exponentials. Indeed we establish a slightly stronger and more general bound that applies to sums of the form \({\sum_{n=M+1}^{M+N}f(\alpha n)\chi(n)}\), where χ is a non-principal character to the modulus p and f is a smooth 1-periodic function.

Mathematics Subject Classification (2000)

Primary 11L05 Secondary 11L40 


Character sums Burgess estimate 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Facultad de CienciasUniversidad Autónoma de MadridMadridSpain

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