1. CMB 2009 (vol 52 pp. 186)
 Broughan, Kevin A.

Extension of the Riemann $\xi$Function's Logarithmic Derivative Positivity Region to Near the Critical Strip
If $K$ is a number field with $n_k=[k:\mathbb{Q}]$, and $\xi_k$
the symmetrized
Dedekind zeta function of the field, the inequality
$$\Re\,{\frac{ \xi_k'(\sigma + {\rm i} t)}{\xi_k(\sigma
+ {\rm i} t)}} > \frac{ \xi_k'(\sigma)}{\xi_k(\sigma)}$$ for $t\neq 0$ is
shown
to be true for $\sigma\ge 1+ 8/n_k^\frac{1}{3}$ improving the result of
Lagarias where the constant in the inequality was 9. In the case $k=\mathbb{Q}$
the
inequality is extended to $\si\ge 1$ for all $t$ sufficiently large or small
and to the region $\si\ge 1+1/(\log t 5)$ for all $t\neq 0$. This
answers positively a question posed by Lagarias.
Keywords:Riemann zeta function, xi function, zeta zeros Categories:11M26, 11R42 
