Hilbert Poincaré series and kernels for products of L-functions

2024/01/02 by Mingkuan Zhang, Yichao Zhang, Zhang, Mingkuan +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.01282

openalex publication_date 2024/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Hilbert Poincaré series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincaré series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincaré series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant.

Related

• Kernels for products of Hilbert L-functions
• On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight
• Poincaré and Eisenstein series for Jacobi forms of lattice index
• Kernels of L-functions of cusp forms
• Hilbert Eisenstein series as Doi-Naganuma lift