Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 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

Uniform Diophantine approximation and run-length function in continued fractions (2301.05855v1)

Published 14 Jan 2023 in math.NT

Abstract: We study the multifractal properties of the uniform approximation exponent and asymptotic approximation exponent in continued fractions. As a corollary, %given a nonnegative reals $\hat{\nu},$ we calculate the Hausdorff dimension of the uniform Diophantine set $$\mathcal{U}(y,\hat{\nu})=\Big{x\in[0,1)\colon \forall N\gg1, \exists~ n\in[1,N], \text{ such that } |T{n}(x)-y|<|I_{N}(y)|{\hat{\nu}}\Big}$$ for algebraic irrational points $y\in[0,1)$. These results contribute to the study of the uniform Diophantine approximation, and apply to investigating the multifractal properties of run-length function in continued fractions.

Summary

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