Estimate of the module of analogue Weyls trigonometrical sum in ring of Gaussian numbers

Abstract

The ring of Gaussian numbers is considered. The estimation of the module of some analogue of Weyl's trigonometrical sum with summation on Gaussian numbers is proved by methods of the analytical number theory. Multiplicative norm of Gaussian numbers is less than some integer.

Keywords

• ring of Gaussian numbers
• trigonometrical sums of G.Weyl