Periods of Hilbert Modular forms, Kronecker series and Cohomology

2021/01/16 by YoungJu Choie, Choie, YoungJu
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2101.06357

Abstract

Generalizing a result of \citeZ1991, CPZ about elliptic modular forms, we give a closed formula for the sum of all Hilbert Hecke eigenforms over a totally real number field with strict class number 1, multiplied by their period polynomials, as a single product of the Kronecker series.

Related

• Twisted Kronecker series and periods of modular forms on Γ₀(N)
• Periods of modular forms on Γ₀(N) and products of Jacobi theta functions
• Periods of Jacobi forms and Hecke operator
• Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
• Les Variétés de Hecke-Hilbert aux points classiques de poids 1