Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with transcendental-number-theory
Search options not deleted
user 26522
8
votes
Accepted
On the irrationality measure of $\sum_{n=1}^\infty a^{-b^n}$
This result is due originally to K. Mahler, and holds true more generally with any algebraic $a$ having $|a| > 1$ (so that the series converges absolutely). I can recommend Masser's lecture in the CIM …
- 13.8k
6
votes
Accepted
Transcendence of a ratio of p-adic logarithms
This is a typical case of the $p$-adic Four Exponentials conjecture. It is surely true, but the proof is beyond reach. If you add in a third prime (equality of $\log_p{x_i} / \log_p{\ell_i}$ for $i = …
- 13.8k
2
votes
Small values of a polynomial evaluated at roots of unity
As in Baker's theorem $|\prod_i \alpha_i^{n_i}-1| \gg n^{-C}$, $n := \max_i{|n_i|}$, this would be another instance where the trivial Liouville lower bound (exponential in $-n$) should actually be rep …
- 13.8k
1
vote
Small values of a polynomial evaluated at roots of unity
After a couple of failed attempts at a proof, I have come to appreciate the difficulty of even the subexponential bound $e^{-o(n)}$.
The lemma I had asserted does not follow from the Theorem below if …
- 13.8k