In this paper we examine curves defined over a field of characteristic $2$ which are ${\left(\mathrm{\mathbb{Z}}/2\mathrm{\mathbb{Z}}\right)}^2$-covers of the projective line. In particular, we determine which $2$-ranks occur for such curves of a given genus and where possible we give explicit equations for such curves. As a corollary, we show that there exist hyperelliptic curves of genus $g$ and $2$-rank $\sigma$ which contain an additional involution in their automorphism group if and only if $g\equiv \sigma (\mathrm{mod} 2)$.

A new short proof of the solvability of the Skolem problem for two by two matrices is given.

The original criteria of Riesz and of Hardy-Littlewood concerning the truth of the Riemann Hypothesis (RH) are revisited and further investigated in light of the recent formulations and results of Maslanka and of Baez-Duarte concerning a representation of the Riemann Zeta function. Then we introduce a general set of similar functions with the emergence of Poisson-like distributions and we present some numerical experiments which indicate that the RH may barely be true.

The paper deals with random vectors $\mathit{X}$ possessing the stochastic representation $\mathit{X}\mathbf{=}R\mathcal{U}$ where $R$ is a positive random radius and $\mathcal{U}$ is a $L_p$-norm generalised symmetrised Dirichlet random vector independent of $R$. The Kotz Type I multivariate distribution appears prominently in the asymptotic results.

A scalar sequence $\left(a_i\right)$ is said to be a $p$-multiplier of a Banach space $X$, if it satisfies the following condition:

In this paper we will prove the following: every bounded linear operator from Banach space $l_1$ into $m_1\left(l_1\right)$, is an absolutely summing operator.