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 Online first
 Sebbar, Abdellah; AlShbeil, Isra

Elliptic Zeta functions and equivariant functions
In this paper we establish a close connection between three
notions attached to a modular subgroup. Namely the set of weight
two meromorphic modular forms, the set of equivariant functions
on the upper halfplane commuting with the action of the modular
subgroup and the set of elliptic zeta functions generalizing
the Weierstrass zeta functions. In particular, we show that the
equivariant functions can be parameterized by modular objects
as well as by elliptic objects.
Keywords:modular form, equivariant function, elliptic zeta function Categories:11F12, 35Q15, 32L10 

3. 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 

4. CMB 2008 (vol 51 pp. 627)
 Vidanovi\'{c}, Mirjana V.; Tri\v{c}kovi\'{c}, Slobodan B.; Stankovi\'{c}, Miomir S.

Summation of Series over Bourget Functions
In this paper we derive formulas for summation of series involving
J.~Bourget's generalization of Bessel functions of integer order, as
well as the analogous generalizations by H.~M.~Srivastava. These series are
expressed in terms of the Riemann $\z$ function and Dirichlet
functions $\eta$, $\la$, $\b$, and can be brought into closed form in
certain cases, which means that the infinite series are represented
by finite sums.
Keywords:Riemann zeta function, Bessel functions, Bourget functions, Dirichlet functions Categories:33C10, 11M06, 65B10 

5. CMB 2008 (vol 51 pp. 334)
6. CMB 2008 (vol 51 pp. 100)
 Petkov, Vesselin

Dynamical Zeta Function for Several Strictly Convex Obstacles
The behavior of the dynamical zeta function $Z_D(s)$ related to
several strictly convex disjoint obstacles is similar to that of the
inverse $Q(s) = \frac{1}{\zeta(s)}$ of the Riemann zeta function
$\zeta(s)$. Let $\Pi(s)$ be the series obtained from $Z_D(s)$ summing
only over primitive periodic rays. In this paper we examine the
analytic singularities of $Z_D(s)$ and $\Pi(s)$ close to the line $\Re
s = s_2$, where $s_2$ is the abscissa of absolute convergence of the
series obtained by the second iterations of the primitive periodic
rays. We show that at least one of the functions $Z_D(s), \Pi(s)$
has a singularity at $s = s_2$.
Keywords:dynamical zeta function, periodic rays Categories:11M36, 58J50 

7. CMB 2007 (vol 50 pp. 11)
 Borwein, David; Borwein, Jonathan

van der Pol Expansions of LSeries
We provide concise series representations for various
Lseries integrals. Different techniques are needed below and above
the abscissa of absolute convergence of the underlying Lseries.
Keywords:Dirichlet series integrals, Hurwitz zeta functions, Plancherel theorems, Lseries Categories:11M35, 11M41, 30B50 

8. CMB 2003 (vol 46 pp. 95)
 Gauthier, P. M.

Cercles de remplissage for the Riemann Zeta Function
The celebrated theorem of Picard asserts that each nonconstant entire
function assumes every value infinitely often, with at most one
exception. The Riemann zeta function has this Picard behaviour in a
sequence of discs lying in the critical band and whose diameters tend
to zero. According to the Riemann hypothesis, the value zero would be
this (unique) exceptional value.
Keywords:cercles de remplissage, Riemann zeta function Category:30 
