bio | website | ma.utexas.edu/users/voloch |
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location | ||
age | ||
visits | member for | 5 years, 7 months |
seen | 21 hours ago | |
stats | profile views | 11,606 |
<-------- Over there, you'll find my website.
Jul 21 |
reviewed | Close Mathjax vs Katex |
Jul 20 |
comment |
When is the image of an integral polynomial contained in the image of another?
In particular, a paper of Bilu and Tichy (Acta Arith, XCV 2000) is relevant. |
Jul 20 |
comment |
When is the image of an integral polynomial contained in the image of another?
The curve $f(x)=g(y)$ will have infinitely many integral points so will be reducible or have genus zero. Google irreducibility of $f(x)-g(y)$ for many papers on this. |
Jul 9 |
reviewed | Reopen Exotic group topologies on the affine group $ax+b$ |
Jul 6 |
comment |
Bound of Chebyshev function and zeros of zeta function
No such $\alpha$ is known unconditionally. |
Jul 1 |
reviewed | Close What conditions imply that a function over $\mathbb{Z}$ is a polynomial? |
Jun 28 |
awarded | Nice Answer |
Jun 28 |
reviewed | Close How to write an abstract for a math paper? |
Jun 21 |
comment |
The significance of the Parvaresh-Vardy curve
Could you make the question self-contained? In particular, what are $E,f,Q$, how do you define the curve? |
Jun 16 |
awarded | Good Answer |
Jun 15 |
awarded | Enlightened |
Jun 15 |
awarded | Nice Answer |
Jun 15 |
awarded | Nice Answer |
Jun 15 |
answered | Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$? |
Jun 14 |
comment |
Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$?
Apply Schanuel to $2\pi i, \log n, \log m$. The last two numbers are linearly independent over $\mathbb{Q}$ because of your hypothesis and the fact that $\pi$ is irrational. Then all three numbers are linearly independent over $\mathbb{Q}$ since $2\pi i$ is not real. Finally, the exponentials of all three numbers are rational, so Schanuel implies that the three numbers are algebraically independent over $\mathbb{Q}$ which is stronger than what you want. |
Jun 14 |
comment |
Can we find two positive integers $n$ and $m$ ($n,m>1$) such that $n^\pi = m$?
This follows from Schanuel's conjecture but it's probably hard to prove unconditionally. |
May 22 |
answered | Is g( ) rational if it looks that way on a large rational subset? |
May 22 |
comment |
Is g( ) rational if it looks that way on a large rational subset?
@DavidHolmes The question makes sense. Maybe it's clearer to ask whether, given the conditions, there is a rational function $g_1$ satisfying the same hypotheses as $g$. |
Apr 29 |
answered | Examples of quotients by infinitesimal group schemes |
Apr 20 |
comment |
Parity-check matrix for code with variable block size and minimum distance
The main conjecture of MDS codes states that there is no code with length + 1 = dimension + min. distance (writing out since your notation is nonstandard) for length > q+2. You want to relax this to length=dim. + distance but want length up to $q^2$. I doubt it can be done. |