1. CMB Online first
 Maier, Helmut; Rassias, Michael Th.

On the size of an expression in the NymanBeurlingBÃ¡ezDuarte criterion for the Riemann Hypothesis
A crucial role in the NymanBeurlingBÃ¡ezDuarte approach to
the Riemann Hypothesis is played by the distance
\[
d_N^2:=\inf_{A_N}\frac{1}{2\pi}\int_{\infty}^\infty
\left1\zeta A_N
\left(\frac{1}{2}+it
\right)
\right^2\frac{dt}{\frac{1}{4}+t^2}\:,
\]
where the infimum is over all Dirichlet polynomials
$$A_N(s)=\sum_{n=1}^{N}\frac{a_n}{n^s}$$
of length $N$.
In this paper we investigate $d_N^2$ under the assumption that
the Riemann zeta function has four nontrivial zeros off the
critical line.
Keywords:Riemann hypothesis, Riemann zeta function, NymanBeurlingBÃ¡ezDuarte criterion Categories:30C15, 11M26 

2. CMB 2011 (vol 54 pp. 316)
 Mazhouda, Kamel

The SaddlePoint Method and the Li Coefficients
In this paper, we apply the saddlepoint method in conjunction with
the theory of the NÃ¶rlundRice 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
$$
c_{F}=\frac{d_{F}}{2}(\gamma1)+\frac{1}{2}\log(\lambda
Q_{F}^{2}),\ \lambda=\prod_{j=1}^{r}\lambda_{j}^{2\lambda_{j}},
$$
where $\gamma$ is the Euler's constant and the notation is as below.
Keywords:Selberg class, Saddlepoint method, Riemann Hypothesis, Li's criterion Categories:11M41, 11M06 
