arXiv subjects

Najib Ouled Azaiez

Publications and source records attributed to Najib Ouled Azaiez.

3 recordsLinked to original sources

arXiv2025

On generalized Stirling numbers and special functions

We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta values by rationals with exponentially decreasing error. We establish connections with Hurwitz zeta functions, polylogarithms, harmonic sums, and multiple sums. Finally, we extend our study to q-Stirling numbers, linking them to q-hypergeometric functions and a q-zeta function, revealing new insights in combinatorics and number theory.

math.NT↗

arXiv2019

Quantum algebra from generalized q-Hermite polynomials

In this paper, we discuss new results related to the generalized discrete $q$-Hermite II polynomials $ \tilde h_{n,α}(x;q)$, introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a $q$-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce $q$-Schrödinger operators and give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra $\mathsf{su}_{q}(1, 1)$, using the generators associated with a $q$-deformed generalized para-Bose oscillator.

math-ph↗

arXiv2006

The Ring of Quasimodular Forms for a Cocompact Group

We describe the additive structure of the graded ring $\widetilde{M}_*$ of quasimodular forms over any discrete and cocompact group $Γ\subset \rm{PSL}(2, \RM).$ We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight $k$. This number is constant for $k$ sufficiently large and equals $\dim_{\CM}(I / I \cap \widetilde{I}^2),$ where $I$ and $\widetilde{I}$ are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that $\widetilde{M}_*$ is contained in some finitely generated ring $\widetilde{R}_*$ of meromorphic quasimodular forms with $\dim \widetilde{R}_k = O(k^2),$ i.e. the same order of growth as $\widetilde{M}_*.$

math.NT↗