Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
Coffey, Mark W.
arXiv, 0507042 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-07-17
Classification:  Mathematical Physics 
@article{0507042,
     author = {Coffey, Mark W.},
     title = {Polygamma theory, the Li/Keiper constants, and validity of the Riemann
  Hypothesis},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507042}
}

Coffey, Mark W. Polygamma theory, the Li/Keiper constants, and validity of the Riemann
  Hypothesis. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507042/