A linear lower bound on the gonality of modular curves

Abstract

The result in the title is proven, using the Selberg estimate on the leading eigenvalue of the non-Euclidean Laplacian, and the method of conformal volumes of Li and Yau.

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References in corpus (1)

• d-gonality of modular curves and bounding torsions

Cited by in corpus (5)

• Gonality of the modular curve X1(N)
• On the arithmetic of certain modular curves
• On the canonical degrees of curves in varieties of general type
• The modularity of elliptic curves over all but finitely many totally real fields of degree 5
• Accelerating the Couveignes Rostovtsev Stolbunov key exchange protocol