20,844 reputation
35096
bio website ma.utexas.edu/users/voloch
location
age
visits member for 5 years, 7 months
seen 21 hours ago

<-------- 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.