Zobrazeno 1 - 10
of 69
pro vyhledávání: '"SEBBAR, ABDELLAH"'
Autor:
Besrour, Khalil, Sebbar, Abdellah
In this paper, we explore the modular differential equation $\displaystyle y'' + F(z)y = 0$ on the upper half-plane $\mathbb{H}$, where $F$ is a weight 4 modular form for $\Gamma_0(2)$. Our approach centers on solving the associated Schwarzian equati
Externí odkaz:
http://arxiv.org/abs/2410.14006
Autor:
Besrour, Khalil, Sebbar, Abdellah
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 $s=\pi^2r^2$ with $r=n/m$ being a rational number in reduced form such that $m\geq 7$. This study is carried out by solving
Externí odkaz:
http://arxiv.org/abs/2403.04973
Autor:
Saber, Hicham, Sebbar, Abdellah
In this paper, we show how solutions to explicit algebraic systems lead to solutions to infinite families of modular differential equations.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2302.13459
Autor:
Saber, Hicham, Sebbar, Abdellah
The purpose of this paper is to provide answers to some questions raised in a paper by Kaneko and Koike about the modularity of the solutions of a differential equations of hypergeometric type. In particular, we provide a number-theoretic explanation
Externí odkaz:
http://arxiv.org/abs/2106.10842
Autor:
Saber, Hicham, Sebbar, Abdellah
For every positive integer $r$, we solve the modular Schwarzian differential equation $\{h,\tau\}=2\pi^2r^2E_4$, where $E_4$ is the weight 4 Eisenstein series, by means of equivariant functions on the upper half-plane. This paper supplements previous
Externí odkaz:
http://arxiv.org/abs/2106.06903
Autor:
Sebbar, Abdellah, Saber, Hicham
In this paper, we investigate the non-modular solutions to the Schwarz differential equation $\{f,\tau \}=sE_4(\tau)$ where $E_4(\tau)$ is the weight 4 Eisenstein series and $s$ is a complex parameter. In particular, we provide explicit solutions for
Externí odkaz:
http://arxiv.org/abs/2005.02340
Autor:
Sebbar, Abdellah, Saber, Hicham
This paper concerns the study of the Schwarz differential equation $\{h,\tau \}=s\,E_4(\tau)$ where $E_4$ is the weight 4 Eisenstein series and $s$ is a complex parameter. In particular, we determine all the values of $s$ for which the solutions $h$
Externí odkaz:
http://arxiv.org/abs/2002.00493
Autor:
Sebbar, Abdellah, Besrour, Khalil
In this paper we give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free and a formula for their conjugacy classes. We do so by exhibiting a correspondence between these groups a
Externí odkaz:
http://arxiv.org/abs/1910.03050
Autor:
Sebbar, Abdellah, Al-Shbail, Isra
In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the mo
Externí odkaz:
http://arxiv.org/abs/1705.10214
Autor:
Saber, Hicham, Sebbar, Abdellah
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 April 2022 508(2)
