Computing Puiseux Expansions at Cusps of the Modular Curve X0(N)
Mark van Hoeij
TL;DR
This paper presents an efficient algorithm for computing Puiseux expansions at cusps of the modular curve X0(N), leveraging a universal relation with hypergeometric functions for any level N.
Contribution
It introduces a novel algorithm that efficiently computes Puiseux expansions at cusps of X0(N) using hypergeometric functions, applicable to all N.
Findings
Algorithm significantly improves computation speed.
Works uniformly for all levels N.
Establishes a new relation with hypergeometric functions.
Abstract
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 any N.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Cryptography and Residue Arithmetic · Polynomial and algebraic computation