Quasi Fibonacci approximation to the low tiny fluctuations of the Li-Keiper coefficients: a numerical computation

TL;DR

This paper investigates the low fluctuations of Li-Keiper coefficients using numerical methods and explores potential advanced approximation techniques for better understanding.

Contribution

It introduces a numerical approach analyzing the tiny fluctuations of Li-Keiper coefficients via discrete derivatives and compares series expansions for improved approximations.

Findings

Numerical results indicate promising directions for more sophisticated approximations.

Analysis of series expansions provides insights into the behavior of Li-Keiper coefficients.

Comparison with exact series highlights potential for refined approximation methods.

Abstract

Using the first discrete derivatives for the expansion in z=0 of the oscillating part lambdatiny(n) =lambda n* of the "tiny" Li-Keiper coefficients , we analyse two series in the variable z=1-1/s ~0 for the first low values and compare them with the exact series. The numerical results suggest interesting more "sophisticated" approximations.