Hoedan

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visits member for 2 years, 6 months
seen Mar 5 '12 at 16:36

Jul
2
awarded  Curious
May
14
awarded  Teacher
Mar
18
awarded  Nice Question
Mar
1
accepted the discriminant of a function field extension
Mar
1
accepted Are these two notions of Galois morphism the same
Mar
1
asked Are these two notions of Galois morphism the same
Mar
1
asked Bound for the Legendre function of the second kind of degree $1/2$
Feb
29
comment An open set in a space is homeomorphic to $S^1$. Is the set close?
Is $M$ connected? Suppose that $M$ is connected. If $U$ is closed in $M$, then $U$ will be an open and closed set inside $M$, and therefore $M=U$.
Feb
28
comment Is there an algebraic reason why a torus can't contain a projective space?
A complex torus of dimension 1 (i.e., an elliptic curve) cannot contain a projective space because the function field of projective space would have to equal the function field of the complex torus. (I assume you want your complex torus contain a projective space as an open subset.) The same argument also holds in higher dimension. I don't know if it is "algebraic: enough though.
Feb
28
comment Bounding the number of integer solutions of the following inequality
It probably is related to the number of lattice points in $\mathbf{Z}^4$ within a circle of radius $r$. The exact number is hard to determine (even though there are explicit formulas), but giving a bound on this number is easy. Namely, the number of integer solutions to $a^2+b^2+c^2+d^2 \leq r$ is bounded by $8\sqrt{r}+8$.
Feb
28
revised Bounding the number of integer solutions of the following inequality
added 55 characters in body
Feb
28
comment Bounding the number of integer solutions of the following inequality
You are completely right. There are (fortunately for me!!) some constraints on $a,b,c,d$. Namely, $ad-bc = 1$ and $(a,b,c,d) = (1,0,0,1) \mod 2$
Feb
28
asked Bounding the number of integer solutions of the following inequality
Feb
27
revised the discriminant of a function field extension
added 9 characters in body
Feb
27
comment the discriminant of a function field extension
I meant (branched) cover.
Feb
27
asked the discriminant of a function field extension
Feb
25
comment Elliptic curves with finitely many rational points
You're right, I slightly misunderstood the question. I guess it was already known to the OP that there are infinitely many ell curves with finitely many rational points over $\mathbf{Q}$. The question of parametrizing such a family is a more difficult question.
Feb
25
answered Elliptic curves with finitely many rational points
Feb
24
awarded  Editor
Feb
24
comment Do gonal morphisms have non-trivial automorphisms
You're right. I changed it. (The case $g=0$ is automatically excluded because $\mathbf{P}^1$ has gonality $0$.)