54 citations · 220 across the 21 of their papers we have counts for
25 papers
Solving Third Order Linear Difference Equations in Terms of Second Order Equations
Heba Bou KaedBey, Mark van Hoeij, Man Cheung Tsui
We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in ter…
Solving Order 3 Difference Equations
Heba Bou KaedBey, Mark van Hoeij, Man Cheung Tsui
We classify order linear difference operators over that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion…
Hypergeometric Solutions of Linear Difference Systems
Moulay Barkatou, Mark van Hoeij, Johannes Middeke +1
We extend Petkovšek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems , with ,…
Submodule approach to creative telescoping
Mark van Hoeij
This paper proposes ideas to speed up the process of creative telescoping, particularly when the telescoper is reducible. One can interpret telescoping as computing an annihilator…
A hyperelliptic saga on a generating function of the squares of Legendre polynomials
Mark van Hoeij, Duco van Straten, Wadim Zudilin
We decompose the generating function of the squares of Legendre polynomials as a product of periods of hyperelliptic curves. These periods…
Sporadic Cubic Torsion
Maarten Derickx, Anastassia Etropolski, Mark van Hoeij +2
Let be a number field, and let be an elliptic curve over . The Mordell--Weil theorem asserts that the -rational points of form a finitely generated abeli…
Functional Decomposition using Principal Subfields
Luiz E. Allem, Juliane Capaverde, Mark van Hoeij +1
Let be a univariate rational function. It is well known that any non-trivial decomposition , with , corresponds to a non-trivial subfield $K(f(t…
Reduction-Based Creative Telescoping for Fuchsian D-finite Functions
Shaoshi Chen, Mark van Hoeij, Manuel Kauers +1
Continuing a series of articles in the past few years on creative telescoping using reductions, we adapt Trager's Hermite reduction for algebraic functions to fuchsian D-finite fun…
Hypergeometric Expressions for Generating Functions of Walks with Small Steps in the Quarter Plane
Alin Bostan, Frédéric Chyzak, Mark van Hoeij +2
We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on defined by a fixed step set that is a subset of the non-zero vect…
The Complexity of Computing all Subfields of an Algebraic Number Field
Jonas Szutkoski, Mark van Hoeij
For a finite separable field extension K/k, all subfields can be obtained by intersecting so-called principal subfields of K/k. In this work we present a way to quickly compute the…
Classifying (almost)-Belyi maps with Five Exceptional Points
Mark van Hoeij, Vijay Jung Kunwar
We classify all rational functions whose branching pattern above {0, 1, infinity} satisfy a certain regularity condition with precisely d=5 exceptions. This work is motivated by so…
The perimeter generating functions of three-choice, imperfect, and 1-punctured staircase polygons
M. Assis, M. van Hoeij, J-M. Maillard
We consider the isotropic perimeter generating functions of three-choice, imperfect, and 1-punctured staircase polygons, whose 8th order linear Fuchsian ODEs are previously known.…
A Modular Algorithm for Computing Polynomial GCDs over Number Fields presented with Multiple Extensions
Mark van Hoeij, Michael Monagan
We consider the problem of computing the monic gcd of two polynomials over a number field L = Q(alpha_1,...,alpha_n). Langemyr and McCallum have already shown how Brown's modular G…
Computing Galois representations and equations for modular curves
Maarten Derickx, Mark van Hoeij, Jinxiang Zeng
We construct plane models of the modular curve , and use their explicit equations to compute Galois representations associated to modular forms for values of that…
Computing Puiseux Expansions at Cusps of the Modular Curve X0(N)
Mark van Hoeij
The goal in this preprint is to give an efficient algorithm to compute Puiseux expansions at cusps of X0(N). It is based on a relation with a hypergeometric function that holds for…
Gonality of the modular curve X1(N)
Maarten Derickx, Mark van Hoeij
In this paper we compute the gonality over Q of the modular curve X1(N) for all N <= 40 and give upper bounds for each N <= 250. This allows us to determine all N for which X1(N) h…
Algorithms and differential relations for Belyi functions
Mark van Hoeij, Raimundas Vidunas
A tool package for computing genus 0 Belyi functions is presented, including simplification routines, computation of moduli fields, decompositions, dessins d'enfant. The main algor…
Belyi functions for hyperbolic hypergeometric-to-Heun transformations
Mark van Hoeij, Raimundas Vidunas
A complete classification of Belyi functions for transforming certain hypergeometric equations to Heun equations is given. The considered hypergeometric equations have the local ex…
On stringy invariants of GUT vacua
James Fullwood, Mark van Hoeij
We investigate aspects of certain stringy invariants of singular elliptic fibrations which arise in engineering Grand Unified Theories in F-theory. In particular, we exploit the sm…
Low Degree Places on the Modular Curve X1(N)
Mark van Hoeij
This short note gives questions and examples of points on X1(N) defined over number fields whose degrees are lower than the gonality.
On Hirzebruch invariants of elliptic fibrations
James Fullwood, Mark van Hoeij
We compute all Hirzebruch invariants for , , and elliptic fibrations of every dimension. A single generating series is produced for each family…
Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations
M. Assis, S. Boukraa, S. Hassani +3
We give the exact expressions of the partial susceptibilities and for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Ya…
Explicit formula for the generating series of diagonal 3D rook paths
Alin Bostan, Frédéric Chyzak, Mark van Hoeij +1
Let denote the number of ways in which a chess rook can move from a corner cell to the opposite corner cell of an three-dimensional chessboard, assuming…
The Ising model: from elliptic curves to modular forms and Calabi-Yau equations
A. Bostan, S. Boukraa, S. Hassani +4
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for ,…