Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.05809

The Exponential World

Garth Warner
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this book there will be found an introduction to transcendental number theory, starting at the beginning and ending at the frontiers. The emphasis is on the conceptual aspects of the subject, thus the effective theory has been more or less completely ignored, as has been the theory of $E$-functions and $G$-functions. Still, a fair amount of ground is covered and while I take certain results without proof, this is done primarily so as not to get bogged down in technicalities, otherwise the exposition is detailed and little is left to the reader.

Explore related subjects

math.HOmath.NT

Keep this discovery

BibTeXRIS

Garth Warner. 2021-05-11. The Exponential World. https://arxiv.org/abs/2105.05809

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Perspectives on the unit distance problem

This is a survey on an old open problem in combinatorics called the unit distance problem, and the field of mathematics around it, called incidence geometry. What do we know about the problem? Why is it difficult? How does it connect with other parts of math?

math.HO↗
arXiv2026

A Categorical Approach to Euclidean Ratios and Proportions

A categorial approach to the non-metric geometry in Books V and VI of Euclid's \textit{Elements} is presented. Specifically, we introduce a diagrammatic syntax that can be overlaid immediately on his diagrams, thus bridging intuitive presentation with fidelity to Euclid's arguments. This syntax makes complicated definitions like V.5, and indeed the arguments throughout books V and VI, including arguments about similar figures, intuitively clear. We show in an appendix that this syntax can be used to solve a puzzle regarding ancient mathematics. Finally, we offer evidence that this approach to Euclidean diagrams is rooted in the Aristotelian tradition itself, and that a similar syntax was utilized, in antiquity, for related questions of numeric and proportions. Thus the syntax is plausibly faithful to Euclid's own thought-world, and not an outside-imposition.

math.HO↗
arXiv2026

Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948

OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 1987 letter from Tutte to Fleischner, the Cycle Double Cover Problem has been open for at least 80 years. Two early results regarding the CDC conjecture were established in one of Tutte's 1949 publications.

math.HO↗