Lucia
Reputation
22,377
Next privilege 25,000 Rep.
 Dec 29 reviewed Leave Open A combinatorial problem Dec 29 comment Asymptotic growth rate of coefficients of generating function Just because the radius of convergence is $\rho$ does not mean that $S(z)$ goes to infinity as $z\to \rho$. For example, consider $\sum_{n=1}^{\infty} z^n/n^2$. Dec 27 comment Asymptotic growth rate of coefficients of generating function Since only odd powers appear here, you probably also want to add in a contribution of the form $(-\rho)^{-n}$ etc. Dec 27 reviewed Leave Open Equation which has nontrivial solutions modulo $N$ for every $N \ge 2$ does not have any nontrivial integer solutions Dec 24 reviewed Close A Chess Question Of The Late Great W.T.Tutte Dec 20 comment Which even numbers are known to be both prime gaps and the sum of 2 primes? Dec 19 reviewed Leave Open Equation which has nontrivial solutions modulo $N$ for every $N \ge 2$ does not have any nontrivial integer solutions Dec 18 comment If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ squarefree? It is absurd that someone chose to vote down this answer! (It took me a little effort to parse your answer -- maybe it would be clearer if the first line said something like: No: if an odd perfect number exists, then $n$ must necessarily contain a square factor.") Dec 18 awarded Enlightened Dec 18 awarded Nice Answer Dec 17 answered What's special about the circle problem? Dec 17 comment What is known about $\sum_{n \leq x} \mu(n) \varphi(n)$? You might need to change your explicit formula a bit -- there'll be $1/\zeta^{\prime}(\rho)$'s in the denominator. So like with the usual partial sums of the Mobius function, this would be a bit more painful to work with than the analogs for $\psi(x)$. Dec 14 awarded Enlightened Dec 14 awarded Nice Answer Dec 14 comment Particular case of the class number formula, Dirichlet characters The first one you can write as $\int_0^1 (1-t^2+t^4-t^6+\ldots) dt = \int_0^1 dt/(1+t^2)$, and compute the integral. The second you can write as $\int_0^1 (1-t-t^2+t^3)/(1-t^5) dt$, and again this is the integral of a rational function which can be computed by partial fractions. (This one is trickier than the first, but still fun -- the substitution $y=t+1/t$ will be useful.) Dec 14 answered Realization of numbers as a sum of three squares via right-angled tetrahedra Dec 13 comment Upper bounds on the difference of consecutive zeta zeros Wasn't this already given in Micah's answer? Dec 13 reviewed Close Testing $0$ for a determinant like function Dec 13 comment Testing $0$ for a determinant like function This is called the permanent and is notoriously hard to compute efficiently. Dec 10 reviewed Leave Open On the Diophantine equation $x^2 = y^p + 2^{r}z^p$ where $p\geq 7$ is an odd prime and $r \geq 2$