On The Function D(s) Associated With Riemann Zeta Function
Journal Title: International Journal of Mathematics and Statistics Invention - Year 2017, Vol 5, Issue 4
Abstract
We consider the function D(s) of the complex argument s=+it, formed with the use of a certain procedure of a transition to the limit. For >1 the function D reduces to the Riemann zeta function, multiplied by the factor (s-1). For <1 the function D is a constant. For =1 function D is undefined. A numerical investigation of D(s) for >1 is presented. "Zeta effect" was discovered-the formation of fictitious short-period oscillations D(s), caused by the confinement of a finite number of terms in the summation of Riemann series containing a large number of harmonics with a slowly varying frequency. A procedure for the numerical suppression of these zeta oscillations is proposed. On the line =1, where D(s) is undefined, an infinite family of "Riemann functions", genetically related to the Riemann zeta function, is introduced. A numerical investigation of these "Riemannian curves" is presented.
Authors and Affiliations
Zarema S. Seidametova, Valerii A. Temnenko
Keywords
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