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 Jul2 awarded Curious May14 awarded Teacher Mar18 awarded Nice Question Mar1 accepted the discriminant of a function field extension Mar1 accepted Are these two notions of Galois morphism the same Mar1 asked Are these two notions of Galois morphism the same Mar1 asked Bound for the Legendre function of the second kind of degree $1/2$ Feb29 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 $M=U$. Feb28 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. Feb28 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 $8\sqrt{r}+8$. Feb28 revised Bounding the number of integer solutions of the following inequality added 55 characters in body Feb28 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 $(a,b,c,d) = (1,0,0,1) \mod 2$ Feb28 asked Bounding the number of integer solutions of the following inequality Feb27 revised the discriminant of a function field extension added 9 characters in body Feb27 comment the discriminant of a function field extension I meant (branched) cover. Feb27 asked the discriminant of a function field extension Feb25 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. Feb25 answered Elliptic curves with finitely many rational points Feb24 awarded Editor Feb24 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 $0$.)