2013/02/28 by Alia Hamieh · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic geometry #Algebraic number field #Analytic Number Theory Research #Discriminant #Ideal class group #Modular form #Modulo #Number theory #Prime (order theory) #Prime ideal #Ring of integers #math.NT #msc:11G40
paper · pdf · doi:10.1007/s00229-014-0696-4
published in manuscripta mathematica 145(3-4), 449-472 (Springer Science+Business Media) · 24 pages
openalex publication_date 2014/09/08 · openalex created_date 2016/06/24 · arxiv created 2016/09/23 · arxiv updated 2016/09/26 · openalex updated_date 2026/08/05
The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic ℤp-extension. Let g be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level N over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant D. We study the l-adic valuation of the special values L(g,χ,(1)/(2)) as χvaries over the ring class characters of K of P-power conductor, for some fixed prime ideal P. We prove our results under the only assumption that the prime to P part of N is relatively prime to D.