In the past two decades, many researchers have studied index 2 Gauss sums, where group generated by characteristic p of underling finite field is in unit Z/mZ for order m multiplicative character involved. A complete solution to problem evaluating sums was given Yang and Xia (2010). particular, it known that some nonzero integral powers this case are quadratic fields. On other hand, Chowla (196...

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially. 4 Author to whom any correspondence should be addressed. New Journal of Physics 13 (2011) 103007 1367-2630/11/103007+37$33.00 © IOP Pu...

By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field F2s without using Davenport–Hasse’s theorem (namely, if s is odd the Gauss sum is −1, and if s is even its value is −(−2)s/2). DOI: https://doi.org/10.4064/ba59-1-02 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-55178 Accepted Ve...

We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These are parallel to that arithmetic of independent and identically distributed random variables previously obtained by Hsu Robbins, Erd\H{o}s, Heyde. apply our Gauss map obtain new asymptotics in theorem L\'evy regular continued fraction expansion irrational numbers $(0,1)$.

The main purpose of this article is to study higher power mean values generalized quadratic Gauss sums using estimates for character sums, analytic methods and algebraic geometric methods. We prove two conjectures which were proposed recently by the above authors in a previous (2022). Here we obtain an asymptotic formula arbitrary means one corresponding moment sum.