Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 57-70.

ON HIGHER ORDER WEIERSTRASS POINTS ON X0(N)

Damir Mikoč and Goran Muić

Department of Teacher Education Studies in Gospić, University of Zadar, dr. Ante Starčevića 12, 53000 Gospić, Croatia
e-mail: dmikoc@unizd.hr

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
e-mail: gmuic@math.hr

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.

2020 Mathematics Subject Classification.   11F11.

Key words and phrases.   Wronskians, holomorphic differentials, cuspidal modular forms.

Full text (PDF) (free access)

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

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