A sharpening of Li's criterion for the Riemann Hypothesis

André Voros

A sharpening of Li's criterion for the Riemann Hypothesis

Number Theory 2007-05-23 v2 Complex Variables

Authors: André Voros

Abstract

Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to \infty$ (with explicit $A>0$ and $B$ ). The approach also holds for more general zeta or $L$ -functions.

Cite

@article{arxiv.math/0404213,
  title  = {A sharpening of Li's criterion for the Riemann Hypothesis},
  author = {André Voros},
  journal= {arXiv preprint arXiv:math/0404213},
  year   = {2007}
}

Comments

1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) S\'er. I. V2: notation corrected in eq.(7); eq.(9) made more precise

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