The distribution of the first elementary divisor of the reductions of a generic Drinfeld module of arbitrary rank

Let $\psi$ be a generic Drinfeld module of rank $r \geq 2$. We study the first elementary divisor $d_{1, \wp}(\psi)$ of the reduction of $\psi$ modulo a prime $\wp$, as $\wp$ varies. In particular, we prove the existence of the density of the primes $\wp$ for which $d_{1, \wp} (\psi)$ is fixed. For $r = 2$, we also study the second elementary divisor (the exponent) of the reduction of $\psi$ modulo $\wp$ and prove that, on average, it has a large norm. Our work is motivated by the study of J.-P. Serre of an elliptic curve analogue of Artin's Primitive Root Conjecture, and, moreover, by refinements to Serre's study developed by the first author and M. R. Murty

Degree bounds for projective division fields associated to elliptic modules with a trivial endomorphism ring

Let $k$ be a global field, let $A$ be a Dedekind domain with $\text{Quot}(A) = k$, and let $K$ be a finitely generated field. Using a unified approach for both elliptic curves and Drinfeld modules $M$ defined over $K$ and having a trivial endomorphism ring, with $k= \mathbb{Q}$, $A = \mathbb{Z}$ in the former case and $k$ a global function field, $A$ its ring of functions regular away from a fixed prime in the latter case, for any nonzero ideal $\mathfrak{a} \lhd A$ we prove best possible estimates in the norm $|\mathfrak{a}|$ for the degrees over $K$ of the subfields of the $\mathfrak{a}$-division fields of $M$ fixed by scalars.Comment: 10 page

The modular degree and the congruence number of a weight 2 cusp form

Let f be a weight 2 normalized newform on the congruence subgroup Γ0(N) with integral Fourier coefficients. There are two important numerical invari-ants attached to f: its congruence number and its modular degree. By definition, the congruence number of f is the largest integer Df suc

Evaluation Study of Professional Burnout among Intensive Care Staff

Background and Aim: Burnout results from chronic exposure to professional stress1, which involves three dimensions: emotional exhaustion, depersonalization, and reduction of personal accomplishments2. It affects many healthcare professionals, with important physical and mental health consequences. Materials and Methods: In 2022, we carried out a study to evaluate the burnout among physicians, nurses, and auxiliary personnel, from all hospital departments. For data collection we used the Maslach Burnout Inventory questionnaire, which measures the three dimensions of the professional burnout syndrome: emotional exhaustion, depersonalization, and personal accomplishment. Results: The study included 235 employees: 34 from the Intensive Care Unit (ICU) and 201 from other departments. A percentage of 58% of the participants were nurses. The results of the analysis of the three dimensions of professional exhaustion for ICU staff reveals mean emotional exhaustion score of 13.2 ± 10.5 (low level), a mean depersonalization score of 1.9 ± 2.8 (low level), and a mean personal accomplishment score of 36.8 ± 5.0 (moderate level). Comparisons of group mean differences across hospital wards demonstrated statistically significant differences in emotional exhaustion, but not in depersonalization or personal accomplishment. No differences were identified according to the professional category of the participants. Conclusions: The study's results demonstrated the existence of a low level of exhaustion and depersonalization in ICU, but also a moderate level of reduced personal achievement. Significant differences between wards in terms of emotional exhaustion have been identified. The results do not confirm the data from the literature, where the incidence of burnout is higher among ICU staff. Further research is needed to identify the local facilitating factors that contribute to reducing the impact of stress in the ICU to support them and implement them in other hospital wards