A. Sebbar

collaborators

5 papers

math.NT2025

Modular differential equations and orthogonal polynomials

Khalil Besrour, Hicham Saber, Abdellah Sebbar

We study second-order modular differential equations whose solutions transform equivariantly under the modular group. In the reducible case, we construct all such solutions using a…

math.NT2025

P-adic Period Conjectures for 1-motives: Integration and Linear Relations

Mohammadreza Mohajer, Abdellah Sebbar

We develop a $p$ -adic theory of periods for 1-motives, extending the classical theory of complex periods into the non-archimedean setting. For 1-motives with good reduction over $p…

math.NT2025

Higher Schwarzian, quasimodular forms and equivariant functions

Hicham Saber, Abdellah Sebbar

The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, k…

math.NT2024

On level 2 Modular differential equations

Khalil Besrour, Abdellah Sebbar

In this paper, we explore the modular differential equation $y^{''} + F (z) y = 0$ on the upper half-plane $H$ , where $F$ is a weight 4 modular form for $I^_{0} (2)$ …

math.NT2024

Hypergeometric solutions to Schwarzian equations

Khalil Besrour, Abdellah Sebbar

In this paper we study the modular differential equation $y^{''} + s E_{4} y = 0$ where $E_{4}$ is the weight 4 Eisenstein series and $s = I ¨ ^{2} r^{2}$ with $r = n / m$ being a rational number in re…