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 Nov 23 awarded Popular Question Oct 19 comment Effective bound of $L(1,\chi)$ Thanks very much -- that's perfect! Oct 18 asked Effective bound of $L(1,\chi)$ Oct 17 awarded Nice Answer Jul 26 comment Is the twisted symmetric fifth power $L$-function holomorphic? @7-adic: Nope -- $Sym^5$ and higher are out of range of Langlands-Shahidi. Basically getting up to $Sym^4$ requires some special cases of Levi subgroups in exceptional groups, and sadly the special cases run out. Garland has a long-term program to try to extend these methods to infinite-dimensional groups -- if one is allowed to use Kac-Moody groups, one could go further. But alas, the results in that direction are not nearly strong enough for $Sym^5$ L-functions as far as I know. Jul 7 comment Why is there a $\sqrt{5}$ in Hurwitz's Theorem? My favorite proof is in Ford's aptly titled article "Fractions" (Amer. Math. Monthly, Vol 45, No 9 (Nov 1938)). He gives the "Ford circle" proof of Dirichlet's approximation theorem, and the $\sqrt{5}$ comes straight out of the geometry he uses. So, if "visual" suffices for "intuitive," this might suffice for your needs. May 21 awarded Nice Answer Feb 24 comment $n$-Cats-in-a-Bed Problem: Picking $n$ points in a given planar domain to maximize the sum of their pairwise distances In the case n=2, a Google image search indicates that pairs of cats in a bed tend not to maximize their pairwise distance. This may be a case of sampling bias however. Feb 23 comment $n$-Cats-in-a-Bed Problem: Picking $n$ points in a given planar domain to maximize the sum of their pairwise distances When $n=1$, the solution can be found at sleepingcatsw.com/images/cats/luther_bed.jpg Jan 26 awarded Yearling Nov 16 comment Weil index computation, p-adic integral These computations should be straightforward, using the explicit formulas of Ranga Rao. See the appendix of "On some explicit formulas in the theory of the Weil representation" in Pacific J. of Math., Vol. 157, No. 2, 1993. Nov 3 comment What are the higher homotopy groups of a K3 suface? A new entry in the encyclopedia of integer sequences, perhaps? Oct 28 comment Visibility interpretation of Riemann zeta zeros on the critical line? You forgot to mention, the fraction of $\mathbb Z$ lattice points visible from the origin is $1 / \zeta(1) = 0$. Oct 26 comment Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section? @Jason: But I guess that by removing a bunch of codim 1 subvarieties from Y, we'd get something $U$ which is "anabelian" or "hyperbolic" in some sense of the word. Then a rational section (existing by anabelian section conjecture) from $P^1 C \rightarrow U$ would extend to a regular section $P^1 C \rightarrow Y$. Again, all contingent on some anabelian conjectures that I don't fully understand. Oct 25 comment Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section? Does this follow from some anabelian conjecture? From such a conjecture, we might expect rational sections $P^1 C \rightarrow Y$ to arise from sections of $Gal(Y) \rightarrow Gal(P^1 C)$ (abs. Galois group of function fields). It's known (Harbater, Pop, Haran, I think) that $Gal(P^1 C)$ is profinite free, and so sections exist. A rational section $P^1 C \rightarrow Y$ gives a regular section by the valuative criterion, right? Or perhaps a counterexample to this type of anabelian conjecture provides a counterexample here? Sep 22 awarded Enlightened Sep 15 comment Results true in a dimension and false for higher dimensions Every cubic polynomial map from $\mathbb C^n$ to $\mathbb C^n$ with nowhere vanishing Jacobian is a bijection. This is true for $n \leq 17$ but fails for larger $n$. Just kidding... but perhaps someday I'll edit the answer, change 17 appropriately and will gain some upvotes. Sep 5 comment Recognize this strange expression from linear algebra? Ahh - or arrgh.. This gets more interesting though. I'll think about how to phrase things in terms of a cocycle. And please don't take offense for the removal of acceptance. I'm also hoping that someone might recognize it from another context and contribute another answer. Sep 3 comment Recognize this strange expression from linear algebra? Wonderful, thank you! (And you did say "cocycle".) Sep 2 comment Recognize this strange expression from linear algebra? Nick - I can only take credit for the pasta-related one. But I'll keep the other to maximize the tag-contribution.