GENERALIZED TWISTED EXPONENTIAL SUM

Author:

Pavel~VARBANETS,~Sergei~VARBANETS

2010 Mathematics Subject Classification:

11L05.

Keywords:

character sum, finite field, Gaussian integers, multiplicative inverse, twisted Kloosterman sum.

Abstract:

We give a bound for generalized twisted Kloosterman sum K_\chi(\alpha,\beta;p^m), p\equiv3\pmod{4}, over the the ring of Gaussian integers \mathbb{G}. Similar sums have been considered by A. Knightly and C. Li over \zz. Our result refines Knightly and Li estimates. Moreover, we obtain a bound for twisted exponential sums with the polynomials over subgroup of elements \alpha from the ring \mathbb{G}/\mathbb{G}_{p^m} under condition N(\alpha)\equiv1\pmod{p^m}. This result may be considered as a continuation of W.-C.W. Li investigations on estimation of the character sum over the subgroup E of \mathbb{F}_{p^m}^\ast consisting of elements whose norms with respect to \mathbb{F}_p are 1.

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Varb-Varb-2013

Vol. 8 (16), 2013