Families of Differential Operators for Overconvergent Hilbert Modular\n Forms

2020/06/03 by Jon Aycock, Aycock, Jon
Mathematics · #11 #14 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.02543

openalex publication_date 2020/06/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We construct differential operators for families of overconvergent Hilbert\nmodular forms by interpolating the Gauss--Manin connection on strict\nneighborhoods of the ordinary locus. This is related to work done by Harron and\nXiao and by Andreatta and Iovita in the case of modular forms and by Zheng Liu\nfor Siegel modular forms. It has applications in particular to p-adic\nL-functions of CM fields.\n

Citations

• Katz type p-adic L-functions for primes p non-split in the CM field

Related

• Gauss-Manin connections for p-adic families of nearly overconvergent modular forms
• p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions
• Overconvergent family of Siegel-Hilbert modular forms
• Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban
• A short note on p-adic families of Hilbert Modular Forms