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Feb
8
comment Advice on dealing with the gap
AA should ask their advisor for advice -- that's what advisors are for!
Feb
7
comment If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
This follows just by partial summation, and would have been known to everyone. For example, how did Chebyshev know that the limit in the prime number theorem, if it exists, must be one?
Feb
5
comment Asymptotics of product of Euler's totient function (A001088)?
Yes and it equals $\frac{1}{e}\prod_p (1-1/p)^{1/p} $.
Feb
2
comment natural radical and an algebraic expression in $\pi$ and/or $e$
I didn't really have anything to add to that one line. By all means include it in the question. (Ok here's one more line to go with my comment: the same constant also appeared in an old asymptotic formula of Bateman to count the number of integers $n$ for which $\phi(n)\le x$. This is why I recognized the Euler product at once, but it is just a coincidence.)
Jan
30
comment natural radical and an algebraic expression in $\pi$ and/or $e$
$\zeta(2)\zeta(3)/\zeta(6)$.
Jan
27
comment Upper bound on answer for Pell equation
You only get from this a bound of $\exp(p^{1/2+\epsilon})$. Please see argument in my answer below.
Jan
15
comment Characters of permutation groups
@GjergjiZaimi: You're probably right. I just didn't know what to call it! But Polya + cycle index covers the bases.
Jan
5
comment Does the antidiagonal in this square matrix always contain a prime?
See mathoverflow.net/questions/217956/… which summarizes what is known.
Dec
29
comment A combinatorial problem
The question at present reads fine to me, but note that this is your fourth attempt at formulating this (in under one hour), and perhaps you could have put in the effort to formulate the question carefully before posting. I can't know of course, but that may have influenced the down vote/close vote.
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
20
comment Which even numbers are known to be both prime gaps and the sum of 2 primes?
See arxiv.org/pdf/1410.8198.pdf
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
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
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
13
comment Upper bounds on the difference of consecutive zeta zeros
Wasn't this already given in Micah's answer?
Dec
13
comment Testing $0$ for a determinant like function
This is called the permanent and is notoriously hard to compute efficiently.
Dec
9
comment On the Diophantine equation $x^2 = y^p + 2^{r}z^p$ where $p\geq 7$ is an odd prime and $r \geq 2$
I just checked it out from a different browser. I didn't encounter any problems in adding any tags to a fake question (while not logged into Mathoverflow). You could ask this in Meta, if indeed you're having some difficulties with the site.
Dec
9
comment On the Diophantine equation $x^2 = y^p + 2^{r}z^p$ where $p\geq 7$ is an odd prime and $r \geq 2$
You mention this about the tags each time you ask a question. But I see no reason why you shouldn't be able to add the tags yourself.
Dec
7
comment “Let” versus “for all”
I have voted to close this as not a research question. I can't really see anyone getting confused by the Theorem given as an example.