Abstract
In this article, we prove an asymptotic formula for the fourth power mean of a general 4-dimensional Kloosterman sum. We use a result of P. Deligne, which counts the number of $$\mathbb {F}_p$$ -points on the surface $$\begin{aligned} (x-1)(y-1)(z-1)(1-xyz)-uxyz=0, ~ u\ne 0, \end{aligned}$$ and then take an average of the error terms over u to prove the asymptotic formula. We also find the number of solutions of certain congruence equations mod p which are used to prove our main result.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.