Integration on valuation fields over local fields

2007/12/13 by Matthew Morrow, Matthew T. Morrow, Morrow, Matthew T.
Mathematics · #11S40 #11S80 (Primary) #20G05 #28C10 #81Q30 (Secondary) #Accounting #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Economics #FOS: Mathematics #Field (mathematics) #Geometry #Local field #Mathematics #Number Theory (math.NT) #Pure mathematics #Residue field #Valuation (finance) #math.AG #math.NT #msc:11S40 #msc:11S80 #msc:20G05 #msc:28C10 #msc:81Q30

paper · pdf · doi:10.48550/arxiv.0712.2172

arxiv created 2007/12/13 · openalex publication_date 2007/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present elements of a theory of translation-invariant integration, measure, and harmonic analysis on a valuation field with local field as residue field. This extends the work of Fesenko. Applications to zeta integrals for two-dimensional local fields are then considered.

Citations

• Fubini's theorem and non-linear change of variables over a two-dimensional local field

Related

• Integration on product spaces and GL_n of a valuation field over a local field
• Integration in valued fields
• Measure and Integration on GL₂ over a Two-Dimensional Local Field
• Corps valués locaux
• Local factors valued in normal domains