Original scientific paper

https://doi.org/10.21857/90836c2xgy

On higher order Weierstrass points on X0(N)

Damir Mikoč ; Department of Teacher Education Studies in Gospić, University of Zadar, dr. Ante Starčevića 12, 53000 Gospić, Croatia
Goran Muić ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Abstract

Let Γ be the Fuchsian group of the first kind. For an even integer m ≥ 4, we describe the space Hm/2(ℜΓ) of m/2–holomorphic differentials in terms of a subspace SmH(Γ) of the space of (holomorphic) cuspidal modular forms Sm(Γ). This generalizes classical isomorphism S2(Γ) ≃ H1(ℜΓ). We study the properties of SmH(Γ). As an application, we describe the algorithm implemented in SAGE for testing if a cusp at ∞ for non–hyperelliptic X0(N) is a m/2-Weierstrass point.

Keywords

Wronskians; holomorphic differentials; cuspidal modular forms

Hrčak ID:

313624

URI

https://hrcak.srce.hr/313624

Publication date:

24.1.2024.

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