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English is not my native tongue. German is not my native tongue. French is not my native tongue.


1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p $ and $p$ is prime which $p>2$?
@zeraouliarafik: I don't think it was asked before, but I am not familiar with the literature of multiperfect numbers.
1d
answered Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p $ and $p$ is prime which $p>2$?
1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p $ and $p$ is prime which $p>2$?
With the notation $m=kn$ your new equation becomes $\sigma(k)/k=n^2$. Hence it would be more natural to ask if there are infinitely many $k$'s for which $\sigma(k)/k$ is a square.
1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p $ and $p$ is prime which $p>2$?
I suggest that you delete this question.
1d
comment Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p $ and $p$ is prime which $p>2$?
It is trivial that $\sigma(k)>k$ for any $k>1$, since $1$ and $k$ are two distinct divisors of $k$. Hence your equation is only satified when $m=n=1$. At any rate, this question is not of research level, voting to close.
2d
revised Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
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2d
revised Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
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2d
revised Is the twisted symmetric fifth power $L$-function holomorphic?
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Jul
26
comment Is the twisted symmetric fifth power $L$-function holomorphic?
For holomorphic forms this was proved in BarnetLamb-Harris-Geraghty-Taylor: A family of Calabi-Yau varieties and potential automorphy II. More precisely, they proved automorphy of the $L$-function apart from finitely many Euler factors.
Jul
26
comment Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
@VesselinDimitrov: You are right, I did not notice "const" in your display, I just focused on the asymptotics. Note that your first display without "const" (i.e. in asymptotic form) is Mertens' first theorem when $K=\mathbb{Q}$.
Jul
26
revised Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
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Jul
26
comment Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
@VesselinDimitrov: Good point. On the other hand, I think deriving Landau's prime ideal theorem is a bit more work than applying partial summation on your first display. In fact, your first two displays are analogues of Mertens' theorems, while the prime number theorem lies soewhat deeper.
Jul
25
comment Elementary Proof of Infinitely many primes $\mathfrak{p} \in \mathbb{Z}[i]$ in the sector $\theta < \arg \mathfrak{p} <\phi $
You are well aware of the equidistribution of Gaussian primes by angle, as your previous question testifies (mathoverflow.net/questions/206707/…). So it is not clear what you are asking. The "cause of a theorem" makes no sense: we are dealing here with mathematics, not theology (in the words of André Weil). At any rate, Dirichlet's theorem and the quoted equidistribution theorem of Hecke have a common source, the nonvanishing of certain $L$-values.
Jul
25
revised Mock modular forms and (indefinite) quadratic forms
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Jul
24
revised A question of Erdős
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Jul
24
comment Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
@TerryTao: Indeed the older results of Frobenius are sufficient, see my response below.
Jul
24
answered Upper density of the set of $n$'s such that $p(n)$ is prime, where $p$ is polynomial
Jul
22
comment Does the proof of Conjectures B and D of Hardy and Littlewood have any implication on the generalized Riemann hypothesis they used?
I completely agree with Greg Martin. In particular, I have never heard of any implication in the other way.
Jul
21
comment Is $\liminf \frac{\sigma_{k}(n)}{n}$ finite for every $k$?
@Ricardo Andrade: I changed back $\sigma_k(n)$ to its originally intended meaning. For the sum of $k$-th powers of $n$ it is trivial that the liminf is infinite.
Jul
21
revised Is $\liminf \frac{\sigma_{k}(n)}{n}$ finite for every $k$?
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