17 citations · 33 across the 14 of their papers we have counts for
12 papers · 1 filter
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…
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 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…
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,…
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…