A Divisor Formula and a Bound on the ℚ-gonality of the Modular Curve X₁(N)

2020/04/28 by van Hoeij, Mark, Smith, Hanson
#11F03 (Secondary) #11G05 #11G16 (Primary) 14H52 #14G35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.13644

Abstract

We give a formula for divisors of modular units on X₁(N) and use it to prove that the ℚ-gonality of the modular curve X₁(N) is bounded above by [(11N²)/(840)], where [\bullet] denotes the nearest integer.

Related

• Gonality of the modular curve X₀(N)
• Tetragonal modular quotients X₀⁺(N)
• A linear lower bound on the gonality of modular curves
• Tetragonal intermediate modular curves
• Low Degree Places on the Modular Curve X1(N)