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<-------- Over there, you'll find my website.


2m
comment Do we know that 'most' finite groups are Galois groups of number fields?
A bunch of specialists are saying I'm wrong, so I must be wrong. I recall a result (of Erdös?) showing that the number of groups of order $2^n$ is some enormous amount and thought that was enough.
1h
comment Twin primes for polynomials in $\Bbb Z[X]$
@DanielHast Most polynomials of content one in $\mathbb{Z}[x]$ and fixed degree are irreducible, so it's even true that given $g_1,\ldots,g_m$ arbitrary, for most $f$, say monic, of fixed degree $> \max \deg g_i$, $f+g_i$ are all irreducible.
1h
comment Do we know that 'most' finite groups are Galois groups of number fields?
Are you asking whether the fact that most groups are $2$-groups has been proved? Yes, it has.
5h
comment Isomorphism problem for two radical extensions
@Lucia and user74230. The answer to the original question was trivially "no", as pointed out by Jeremy in the first comment. The first two or three close votes were given before the question was edited. I am also puzzled by how user74230 managed to post an answer after the question was closed.
1d
reviewed Close $SU(2)$ and the three sphere
2d
reviewed Close Gaussian curvature of a z=f(x,y) function
Nov
24
reviewed Close How to understand mathematics
Nov
24
reviewed Close Diametrically opposite points go to diametrically opposite points under stereographic projection
Nov
23
reviewed Close When is an holomorphy ring a PID?
Nov
23
reviewed Leave Closed Calculating the quotient group $\mathbb{Z}\times\mathbb{Z}/<(1,1),(1,-1)>$
Nov
21
reviewed Leave Closed elliptic curves and tower of finite fields
Nov
21
reviewed Close Summation with 2 functions
Nov
20
comment Is elliptic curve point division defined over the field of real numbers?
Over the reals there are elliptic logarithms and elliptic exponentials that convert the problem to division in real numbers. The only issue is that you can only divide by 2 (or any even number) if you are in the connected component of the identity. This is not an MO question, though.
Nov
20
comment degree of polynomials in nullstellensatz
ams.org/journals/jams/1988-01-04/S0894-0347-1988-0944576-7/…
Nov
19
comment Pairs of quadratic polynomials taking values pairs of consecutive squares
I am not 100% sure that the integral points on the curves you wrote down are stably integral in the sense of Abramovich's paper, but I suspect they are. If they are then, yes, Abramovich's result is precisely that Vojta's conjecture implies boundedness.
Nov
19
comment Pairs of quadratic polynomials taking values pairs of consecutive squares
The boundedness of the number of stably integral points on elliptic curves is an open problem. It follows from the Vojta conjectures (see Abramovich, Inv. Math. 127). I think your points are stably integral. Unboundedness probably implies unbounded rank, which is also open.
Nov
17
reviewed Close Tetris in 3D with 5 units
Nov
17
comment Reducible polynomials
I think you should clarify the question. Miller-Rabin outputs "composite" or "probable prime", composite is certain, probable prime is not. The actual probability depends on how you perform the test. The stupid algorithm I suggested in a comment to Igor's answer also returns "composite" (rarely) or "probable prime" often but this time with good probability given that most polynomials with integer coeffs are irreducible. If you want a better answer, you need to be more specific. How is the input given? What running time do you want? and so on.
Nov
17
comment Reducible polynomials
What's wrong with LLL?
Nov
17
comment Reducible polynomials
@Turbo If you want a probabilistic test, just compute the gcd of the coefficients and output "irreducible" if the result is 1. It works with probability 1.