bio | website | ma.utexas.edu/users/voloch |
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visits | member for | 5 years, 1 month |
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stats | profile views | 10,984 |
<-------- Over there, you'll find my website.
Jan 10 |
awarded | Nice Answer |
Jan 9 |
comment |
What is the longest recorded gap between “proof” of a “theorem” and discovery that the result is false
Plemelj "solved" Hilbert's 21st problem in 1908 and Bolibrukh gave a counterexample in 1990. But I am going to vote to close. |
Jan 4 |
reviewed | Close Research and exposition: how does writing “basic” books affect your “serious” research work? |
Jan 3 |
comment |
Is it possible on an elliptic curve both $x,y$ to be arbitrary large powers infinitely often?
You are essentially looking for rational points on a curve $f(x^2,y)=0$ or $f(x^2,y^2)=0$ depending on your condition. So you have to work out if the curve has genus 1 or > 1, which depends on whether the obvious cover is unramified or not. This is not an MO question. |
Dec 29 |
comment |
polynomials in many variables and Hasse principle
If $f(x,y)=0$ is a counterexample in two variables then $f(x_1+\ldots+x_n,y)=0$ is also. |
Dec 28 |
reviewed | Close classification of Nilpotent Leibniz Algebra |
Dec 27 |
comment |
More on Vojta's exceptional set for a more general abc conjecture
$q < 1 + \epsilon$ outside of $Z_{\epsilon}$ so $q \le 1$ outside of the union of all $Z_{\epsilon}$. The original ABC which I guess is $n=3$ in your notation doesn't have an excepcional set, you only need it for $n>3$. Meanwhile Michael answered your question. |
Dec 27 |
comment |
More on Vojta's exceptional set for a more general abc conjecture
Your interpretation that $\limsup q = 1$ outside a Zariski closed subset is incorrect. For every $\epsilon > 0$ there is a Zariski closed subset but it depends on $\epsilon$. As $\epsilon \to 0$ the union of these Zariski closed subsets may well be Zariski dense. I haven't looked at your example to see if in fact that's what you are getting. |
Dec 25 |
reviewed | Close Why is $ \frac{\pi^2}{12}=\ln(2)$ not true? |
Dec 24 |
reviewed | Leave Closed The resolution of which conjecture/problem would advance Mathematics the most? |
Dec 22 |
reviewed | Close this complex inequality have some background?and we can find stronger than this inequality? |
Dec 17 |
comment |
Open problems with monetary rewards
As for why 2) is no longer valid, I suspect it's because MacWilliams died in 1990. en.wikipedia.org/wiki/Jessie_MacWilliams |
Dec 17 |
reviewed | Close Graduate program applications that require questionnaires and other non-letter material |
Dec 9 |
comment |
Algebraic equivalence vs linear equivalence
For smooth projective complex varieties, this is the same as the Picard variery (or equivalently the Albanese) is zero, almost by definition. As the dimension of the Picard variety is the first Betti number, here is your criterion: $b_1=0$. |
Dec 9 |
comment |
Have there been any new developments in the Firoozbakht conjecture?
@KarlSchwede As explained in Carlo's answer, this is slighty stronger than a 80-year old conjecture of Cramer, which is NOT a consequence of the Riemann hypothesis. I don't think you should expect new developments every few years and, if there are, you'll hear about them. |
Dec 9 |
reviewed | Close Have there been any new developments in the Firoozbakht conjecture? |
Dec 6 |
reviewed | Leave Closed The resolution of which conjecture/problem would advance Mathematics the most? |
Dec 4 |
comment |
Good lecture notes/books on Jacobian of hyperelliptic curve
If you want to view things from a more applied standpoint, then Galbraith "Mathematics of public key cryptography" is a good reference. |
Dec 4 |
comment |
Why there are two point at infinity on certain elliptic curve
This is not an MO question. The function field of the quartic has two embeddings in $k((1/x))$ corresponding to $y = \pm x^2 + \cdots$, so two places at infinity. |
Dec 4 |
comment |
minimizing an integral over integer-coefficient polynomials $\displaystyle \inf_{f \in \mathbb{Z}[x]} \int_a^b f(x)^2 \, dx $
Integer valued polynomials is not the same as polynomials with integer coefficients. Which one do you want? |