# DavidLHarden

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## Registered User

 Name DavidLHarden Member for 2 years Seen 12 hours ago Website Location Age 31
Right now, I'm a math grad student at the University of Miami.
 11h comment Criteria for Aut(G) to be simple$M_{24}$ is also a sporadic group with trivial outer automorphism group, so it needs to be added (without any covers, since it has trivial Schur multiplier) to your third family of groups. Jun10 revised Can the unsolvability of quintics be seen in the geometry of the icosahedron?removed a "clearly" Jun10 answered Can the unsolvability of quintics be seen in the geometry of the icosahedron? Jun1 revised Transitive subgroup of $S_p$ containing a $p$-cycle and a double transpositionreplaced an "and" by "or" because it fits more precisely (in parenthetical remark following "dead ends") May30 revised Transitive subgroup of $S_p$ containing a $p$-cycle and a double transpositionshowed that assumptions on orbit structure in adjunction process still hold when process is applied to a transitive group May30 revised Transitive subgroup of $S_p$ containing a $p$-cycle and a double transpositionremoved awkwardly placed list of permutation groups and replaced it with more natural reference to how n >= 9 assumption is used May30 answered Transitive subgroup of $S_p$ containing a $p$-cycle and a double transposition Mar20 comment Known and unknown about Ramanujan’s tau functionThe mod $\l$ representation of what group is degenerate modulo 691? 691 doesn't divide the order of any Conway group -- indeed, no prime exceeding 71 divides the order of a sporadic group. Mar17 comment Known and unknown about Ramanujan’s tau functionYou mean, it's 50-50 for those $n$ such that $\tau(n) \neq 0$. If there is a prime $p$ such that $\tau(p) = 0$, then multiplicativity of $\tau$ yields $\tau(pm) = 0$ whenever $m$ is a nonmultiple of $p$, giving a set of density $\frac{1}{p} - \frac{1}{p^{2}}$ on which $\tau$ vanishes. Thanks for the update on Sato-Tate. Mar16 asked Known and unknown about Ramanujan’s tau function Mar5 awarded ● Popular Question Feb26 comment Can sine be made into a homomorphism?No. $\sin{t} = \sin{\pi - t}$ for all real numbers $t$, so the kernel of your homomorphism would contain the difference $\pi - 2t$ for all real numbers $t$. Since the kernel is all of $\mathbb{R}$, the homomorphism must be trivial. You can try to remedy this by taking an appropriate linear combination of sine and cosine, but the only examples of this which should work are those which are scalar multiplies of $\cos{t} + i \cdot \sin{t} = e^{i \cdot t}$. Jan29 awarded ● Yearling Jan15 comment Real symmetric matrix has at least one real eigenvalue - an elementary algebraic, non-complex proof.What do you mean by "analytic methods"? What algebraic properties of the real numbers would you appeal to to distinguish it from fields for which this is not true, if you don't use properties established by using what's usually called analysis? For example, if you allow the Intermediate Value Theorem, you can reduce to the case where you consider a $2n \times 2n$ matrix. But this is analytic, since it is proven by noting that polynomials are continuous functions. Dec30 asked A non-commutative ring from SU(2) Dec25 comment Is there another proof for Dirichlet’s theorem?I am surprised no one has mentioned dms.umontreal.ca/~andrew/PDF/PNTforaps.pdf in this thread.