54 citations · 220 across the 21 of their papers we have counts for
6 papers · 1 filter
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…
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…
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.