Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergents as approximants in continued fraction expansions of complex
  numbers with Eisenstein integers   Let $\frak E$ denote be the ring of Eisenstein integers. Let $z\in \mathbb C$
and $p_n,q_n \in \frak E$ be such that $\{p_n/q_n\}$ is the sequence of
convergents corresponding to the continued fraction expansion of $z$ with
respect to the nearest integer algorithm. Then we show that for any $q\in \frak
E$ such that $1\leq |q|\leq |q_n|$ and any $p\in \frak E$, $|qz-p|\geq \frac12
|q_nz-p_n|$. This enables us to conclude that $z\in \mathbb C$ is badly
approximable, in terms of Eisenstein integers, if and only if the corresponding
sequence of partial quotients is bounded.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph