Timeline for How many algebraic integers exist with degree $\leq k$ and bounds on the modulus of all Galois conjugates?
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| Nov 26, 2010 at 19:02 | comment | added | ACL | Both papers count algebraic numbers of bounded height which is slightly different from what you want. (The height of $\alpha$, with conjugates $\alpha_j$ ($1\leq j\leq d$) is the logarithm of the Mahler measure of its minimal polynomial; for an algebraic integer, $h(\alpha)= d^ {-1} \sum \log\max(1,|\alpha_j|)$. However, while Schanuel counts elements of a given number field, Masser and Vaaler count elements of degree $k$ over a given number field. For small $k$, or over $\mathbf Q$, one even has asymptotic expansions but basically nothing more precise seems to be known. | |
| Nov 26, 2010 at 18:18 | history | edited | Felipe Voloch | CC BY-SA 2.5 |
added 401 characters in body
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| Nov 26, 2010 at 15:28 | comment | added | Kevin O'Bryant | Are these related? Do they answer the question affirmatively, or suggest that nothing better is known? A little indication of what's in the articles would make the answer much more useful to us lurkers. | |
| Nov 26, 2010 at 13:36 | history | answered | Felipe Voloch | CC BY-SA 2.5 |