location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword Riemann Hypothesis

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2011 (vol 54 pp. 316)

Mazhouda, Kamel
 The Saddle-Point Method and the Li Coefficients In this paper, we apply the saddle-point method in conjunction with the theory of the NÃ¶rlund-Rice integrals to derive precise asymptotic formula for the generalized Li coefficients established by Omar and Mazhouda. Actually, for any function $F$ in the Selberg class $\mathcal{S}$ and under the Generalized Riemann Hypothesis, we have $$\lambda_{F}(n)=\frac{d_{F}}{2}n\log n+c_{F}n+O(\sqrt{n}\log n),$$ with $$c_{F}=\frac{d_{F}}{2}(\gamma-1)+\frac{1}{2}\log(\lambda Q_{F}^{2}),\ \lambda=\prod_{j=1}^{r}\lambda_{j}^{2\lambda_{j}},$$ where $\gamma$ is the Euler's constant and the notation is as below. Keywords:Selberg class, Saddle-point method, Riemann Hypothesis, Li's criterionCategories:11M41, 11M06
 top of page | contact us | privacy | site map |