Mean Values over Lattices in Number Fields and Effective Diophantine Approximation

2023/06/04 by N. J. S. Hughes, Hughes, Nathan · 1 citation
Mathematics · #11H60 #11J68 #37A44 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.02499

openalex publication_date 2023/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We answer a question raised by Alam and Ghosh concerning an error term for a spiralling result in Diophantine approximation by rationals in a number field. The proof relies on a generalisation of Rogers' Mean Value Theorem to algebraic number fields and an effective ergodic theorem due to Gaposhkin.

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• Module lattices and their shortest vectors

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