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
Publication date:
24.1.2024.
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