MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $K=\mathbb{Q}(\alpha)$ is a fixed number field with $[K:\mathbb{Q}]=d$ and fixed basis $b_1,b_2,..,b_d$. Define $$m(\alpha) = max \{ | p_i| , |q_i| : 1 \leq i \leq d \},$$ where the max is taken over all representatives of $\alpha$ of the form $$\alpha = \frac{p_1b_1+p_2b_2+\ldots+p_db_d}{q_1b_1+q_2b_2+\ldots+q_db_d}.$$

Are there any papers which describe techniques to compute this number?

share|cite|improve this question

I'm going to reformat this to use proper TeX formatting, but you should really do this yourself. Just put dollar signs around the math, and if there's a problem, use back-ticks around the dollar signs.

As for your question, once you write down one representation, you can always replace $(p_1,\ldots,p_d,q_1,\ldots,q_d)$ with $(cp_1,\ldots,cp_d,cq_1,\ldots,cq_d)$ for an arbitrary integer $c$, so your quantity $m(\alpha)$ is equal to $\infty$. Maybe you want to specify that $p_1,\ldots,p_d,q_1,\ldots,q_d\in\mathbb{Z}$ and that $\gcd(p_1,\ldots,p_d,q_1,\ldots,q_d)=1$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.