Quantum Modular Forms from Real Quadratic Double Sums

2022/05/05 by Kathrin Bringmann, Bringmann, Kathrin, Caner Nazaroglu +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2205.02643

openalex publication_date 2022/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In 2015, Lovejoy and Osburn discovered twelve q-hypergeometric series and proved that their Fourier coefficients can be understood as counting functions of ideals in certain quadratic fields. In this paper, we study their modular and quantum modular properties and show that they yield three vector-valued quantum modular forms on the group Γ₀ (2).

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