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 language | English |
|---|---|
| Article number | 103231 |
| Number of pages | 30 |
| Journal | Annals of Pure and Applied Logic |
| Volume | 174 |
| Issue number | 4 |
| Early online date | 13 Dec 2022 |
| DOIs | |
| Publication status | Published - 30 Apr 2023 |
Bibliographical note
No funders listed in dashboard record.Funding
The author would like to thank the anonymous referees for their extremely insightful comments on the original version of the paper, which in particular led to the inclusion of a number of additional remarks and points of clarification that have improved the paper considerably.
Keywords
- Applied proof theory
- Dialectica interpretation
- Rates of convergence and metastability
- Tauberian theory
ASJC Scopus subject areas
- Logic