The Structure of Masses of rank n Quadratic Lattices of varying determinant over number fields

2011/08/17 by Jonathan Hanke, Hanke, Jonathan
Mathematics · #11E08 #11E12 #11E41 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT #msc:11E08 #msc:11E12 #msc:11E41

paper · pdf · doi:10.48550/arxiv.1108.3580

39 pages, 4 tables

openalex publication_date 2011/08/17 · arxiv created 2011/09/27 · arxiv updated 2011/09/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we establish a fundamental structural result for formal series encoding the total non-archimedean masses of quadratic lattices of varying determinant squareclasses, but with fixed rank n and signature over any fixed number field. We conclude with some local computations for n=2, and use these to derive an analytic class number formula for CM extensions.

Citations

• Notes on "Quadratic Forms and Automorphic Forms" from the 2009 Arizona Winter School
• A proof of the S-genus identities for ternary quadratic forms
• On Modular Forms of Half Integral Weight

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