17 citations · 33 across the 14 of their papers we have counts for
20 papers
Higher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker Functions
Hicham Saber, Abdellah Sebbar
We determine the Aharonov invariants of order at least two of every elliptic double cover by evaluating its projective kernel. In orders at least three, the formula separates the i…
Projective Kernels and Replicability in Modular Function Theory
Hicham Saber, Abdellah Sebbar
We introduce a projective-kernel framework for the study of replicable functions in modular function theory. The main point is that the same two-point kernel simultaneously encodes…
Reducible modular differential equations, Jacobi pole divisors, and supersingular lifts
Khalil Besrour, Hicham Saber, Abdellah Sebbar
We study the reducible parameter values of a second-order modular differential equation for the full modular group and show that their pole data is controlled by a single polynomia…
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…
On a Conjecture Concerning the Complementary Second Zagreb Index
Hicham Saber, Tariq Alraqad, Akbar Ali +2
The complementary second Zagreb index of a graph is defined as , where denotes the degree of a vertex in and…
Modular differential equations and algebraic systems
Hicham Saber, Abdellah Sebbar
In this paper, we show how solutions to explicit algebraic systems lead to solutions to infinite families of modular differential equations.
On the Maximum Atom-Bond Sum-Connectivity Index of Graphs
Tariq Alraqad, Hisham Saber, Akbar Ali +1
The atom-bond sum-connectivity (ABS) index of a graph with edges is the sum of the numbers over , where is…
Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices
Tariq A. Alraqad, Igor Z. Milovanovic, Hicham Saber +3
Let be the degree of a vertex of a graph . The atom-bond sum-connectivity (ABS) index of a graph is the sum of the numbers over all edg…
On the modularity of solutions of certain differential equations of hypergeometric type
Hicham Saber, Abdellah Sebbar
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 hyperge…
Equivariant solutions to modular Schwarzian equations
Hicham Saber, Abdellah Sebbar
For every positive integer , we solve the modular Schwarzian differential equation , where is the weight 4 Eisenstein series, by means of equivariant f…
On Graded s-Prime Submodules
Hicham Saber, Tariq Alraqad, Rashid Abu-Dawwas
In this article, we introduce the concepts of graded -prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to…
Graded -Submodules
Tariq Alraqad, Hicham Saber, Rashid Abu-Dawwas
Let be a group with identity and a commutative -graded ring with a nonzero unity . In this article, we introduce the concepts of graded -submodules and graded…
Intersection Graph of Graded ideals
T. Alraqad, H. Saber, R. Abu-Dawwas
In this article we introduce and study the intersection graph of graded ideals of graded rings. The intersection graph of graded ideals of a graded ring is a simple gra…
Graded Rings
Tariq Alraqad, Hicham Saber, Rashid Abu-Dawwas
The main goal of this article is to introduce the concept of graded rings. This concept is an extension of the notion of rings. Let be a group and be a grad…
Automorphic Schwarzian equations and integrals of weight 2 forms
Abdellah Sebbar, Hicham Saber
In this paper, we investigate the non-modular solutions to the Schwarz differential equation where is the weight 4 Eisenstein series and is a complex…
Automorphic Schwarzian equations
Abdellah Sebbar, Hicham Saber
This paper concerns the study of the Schwarz differential equation where is the weight 4 Eisenstein series and is a complex parameter. In particular,…
On the Structure of Finite Groups Associated to Regular Non-Centralizer Graph
Tariq A. Alraqad, Hicham Saber
The non-centralizer graph of a finite group is the simple graph whose vertices are the elements of with two vertices and are adjacent if their centralizers ar…
Equivariant functions for the Möbius subgroups and applications
Hicham Saber
The aim of this paper is to give a generalization of the theory equivariant functions, initiated in [17, 4], to arbitrary subgroups of PSL2(R). We show that there is a deep relatio…
Equivariant functions and vector-valued modular forms
Hicham Saber, Abdellah Sebbar
For any discrete group and any 2-dimensional complex representation of , we introduce the notion of equivariant functions, and we show that they are parameterized by…
Vector-valued automorphic forms and vector bundles
Hicham Saber, Abdellah Sebbar
While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group and an arbitrary representation of in GL, their existence has been…