MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Estimate of the module of analogue Weyl’s trigonometrical sum in ring of Gaussian numbers

P. N. Sorokin

Scientific-Research Institute for System Studies, Russian Academy of Sciences (NIISI RAN), Nakhimovskii av. 36-1, Moscow, 117218, Russia

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.

UDC: 511.3

Received: 27.06.2010

DOI: 10.20537/2076-7633-2010-2-4-343-347