Blocks Partition Analysis: A Possible Positivity of the Li-Keiper Coefficients


Authors: Danilo Merlini, Luca Rusconi, Massimo Sala, and Nicoletta Sala
Page Range: 95-105
Published in: Chaos and Complexity Letters, 16#2
ISSN: 1556-3995

Table of Contents

We develop an expression for the Li-Keiper coefficients λn in terms of k-blocks partitions, to begin with, for low values of n.
The k-blocks partitions are given in terms of our cluster functions φn and the main point of this work lies in the emergence of an alternating sequence of values converging toward values of λn near the true values, i.e., increasing the index k of the blocks one obtains an increasing range of positivity of the Li-Keiper coefficients.
With the contribution of k = 1 and k = 2 blocks, positivity of the λn is reached already until n = 26-27.
The treatment is given here until k = 4 blocks up to n = 30. λn are all found to be positive.

Keywords: Infinite set of Equations at s = 1, cluster functions grow, blocks partitions, Li-Keiper coefficients, Riemann Hypothesis

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