arXiv subjects

Merlini Danilo

Publications and source records attributed to Merlini Danilo.

3 recordsLinked to original sources

arXiv2020

Infinite set of non linear Equations for the Li- Keiper Coefficients: a possible new upper and lower bound

Starting with an infinite set of non linear Equations for the Li-Keiper coefficients, we first specify a lower bound emerging from the infinite set and give a characterization of it. Then, we propose a possible new upper and lower bound for the coefficients in few of the partitions occurring in the cluster functions furnishing in a nonlinear way the coefficients. A numerical experiment up to n=15 confirms the proposed bounds and an experiment, i.e. the counting of the zeros in the binary representation of an integer for a constant related to the Glaisher-Kinkelin constant is also given up to n=32.

math.GM↗

arXiv2019

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

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.

math.GM↗

arXiv2019

A numerical comment on the 'tiny' oscillations and a heuristic 'conjecture'

In the first part of this short work (in the form of a comment) we add the plots of two more values of the Li-Keiper coefficients lambda5 and lambda6, computed as in our recent work where the first four values were in particular given. This for the trend as well as for the oscillating path ('tiny', the term coined by Maslanka in his pioneering work). Then, in the second part looking at the tiny oscillations, we propose a 'numerical conjecture' in a more strong form, i.e. with a logarithmic behaviour and carry out a short numerical experiment on the new 'numerical conjecture'.

math.NT↗