English

An arithmetic interpretation of generalized Li's criterion

Number Theory 2018-05-25 v3

Abstract

Recently, we have established the generalized Li's criterion equivalent to the Riemann hypothesis, viz. demonstrated that the sums over all non-trivial Riemann function zeroes k_n,a=Sum_rho(1-(1-((rho-a)/(rho+a-1))^n) for any real a not equal to 1/2 are non-negative if and only if the Riemann hypothesis holds true; arXiv:1304.7895 (2013); Ukrainian Math. J., V.66, N3, 371-383 (2014). An arithmetic interpretation of this generalized Li's criterion is given here.

Keywords

Cite

@article{arxiv.1305.1421,
  title  = {An arithmetic interpretation of generalized Li's criterion},
  author = {Sergey K. Sekatskii},
  journal= {arXiv preprint arXiv:1305.1421},
  year   = {2018}
}

Comments

+10 pages. Reasons of replacement: The proof of the Theorem 3 is changed

R2 v1 2026-06-22T00:12:37.427Z