Hyperelliptic Shimura curves and L-functions of central vanishing order at least 3

2025/09/07 by Congling Qiu, Qiu, Congling
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.06175

openalex publication_date 2025/09/07 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We use hyperelliptic Shimura curves to find triple product L-functions of Hilbert newforms with central vanishing orders proved to be at least 3.

Citations

• Ceresa Cycles of X₀(N)
• Faber--Pandharipande cycle, real multiplication and torsion points
• Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles associated to modular curves
• Finiteness properties for Shimura curves and modified diagonal cycles
• Gross--Schoen Cycles and Dualising Sheaves
• Relating invariant linear form and local epsilon factors via global methods

Related

• Determinant Expressions for Hyperelliptic Functions (with an Appendix by Shigeki Matsutani)
• Shimura curves within the locus of hyperelliptic Jacobians in genus\n three
• The functional equation for L-functions of hyperelliptic curves
• Hyperelliptic Kleinian functions and applications
• Vanishing of Dirichlet L-functions at the central point over function fields