A finitization of Littlewood’s Tauberian theorem and an application in Tauberian remainder theory

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Abstract

In this paper we study Littlewood's Tauberian theorem from a proof theoretic perspective. We first use the Dialectica interpretation to produce an equivalent, finitary formulation of the theorem, and then carry out an analysis of Wielandt's proof to extract concrete witnessing terms. We argue that our finitization can be viewed as a generalized Tauberian remainder theorem, and we instantiate it to produce two concrete remainder theorems as a corollary, in terms of rates of convergence and rates metastability, respectively. We rederive the standard remainder estimate for Littlewood's theorem as a special case of the former.

Original languageEnglish
Article number103231
Number of pages30
JournalAnnals of Pure and Applied Logic
Volume174
Issue number4
Early online date13 Dec 2022
DOIs
Publication statusPublished - 30 Apr 2023

Bibliographical note

No funders listed in dashboard record.

Keywords

  • Applied proof theory
  • Dialectica interpretation
  • Rates of convergence and metastability
  • Tauberian theory

ASJC Scopus subject areas

  • Logic

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