Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants c_n, n = 1,2,..., showing in detail that the leading behaviour (1/2) ln n of lambda_n/n is absent in c_n. Additional results are presented, including a novel explicit representation of c_n in terms of the Stieltjes constants gamma_j. We conjecture as to the large-n behaviour of c_n. Should this conjecture hold, validity of the Riemann hypothesis would follow.
Keywords
Cite
@article{arxiv.math-ph/0507042,
title = {Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis},
author = {Mark W. Coffey},
journal= {arXiv preprint arXiv:math-ph/0507042},
year = {2007}
}
Comments
28 pages, 4 figures