Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Irrationality and transcendence of continued fractions with algebraic integers (1902.04312v1)

Published 12 Feb 2019 in math.NT

Abstract: We extend a result of Han\v{c}l, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence ${\alpha_n}$ of algebraic integers of bounded degree, each attaining the maximum absolute value among their conjugates and satisfying certain growth conditions, the condition $$ \limsup_{n \rightarrow \infty} \vert\alpha_n\vert{\frac{1}{Dd{n-1} \prod_{i=1}{n-2}(Ddi + 1)}} = \infty $$ implies that the continued fraction $\alpha = [0;\alpha_1, \alpha_2, \dots]$ is not an algebraic number of degree less than or equal to $D$.

Summary

We haven't generated a summary for this paper yet.