Twisted exponential sums over the ring of Gaussian integers

Author:

Pavel~Varbanets,~Sergey~Varbanets

2010 Mathematics Subject Classification:

11L03, 11L05, 11L07.

Keywords:

Kloosterman sum, norm group, twisted exponential sum.

Abstract:

We obtain formulae and estimates for twisted exponential sums of the form S(\chi,f,p^m)=\sum{\chi(x)}\e^{2\pi{i}\Re{\left({f(x)}/{p^m}\right)}}, where x runs the elements of certain subgroups of the group of residue classes modulo p^m in the ring of Gaussian integers.

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Vol. 10 (18), 2015