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Jan 5 |
comment |
Sums of primes that are themselves prime
@TerryTao: I don't understand how one gets a constant below $1/2$ though. My understanding is that the work of Maynard et al does not yet give positive proportion of tuples. I.e. how does one get a positive proportion of values for which $S(n)$ is a multiple of $3$? (Infinitely many is fine, and really goes back to Daniel Shiu.) |
Jan 5 |
comment |
Sums of primes that are themselves prime
@TerryTao: The sums $S(n)$ alternate in parity. So $P(n)/n$ is trivially at most $1/2$. But what you say would apply to maybe get strictly below $1/2$. |
Jan 5 |
comment |
Sums of primes that are themselves prime
A first step would be to understand how many of the $S(n)$ are multiples of a given number $d$. Already for $d=3$ I don't know how to determine the number of $S(n)$'s that are multiples of $3$. Such questions seem too hard to answer (although one can of course formulate conjectures). |
Jan 4 |
comment |
Submission of papers to ArXiv or similar
You could also look at the answers to this question: mathoverflow.net/questions/35927/… , or add your own answer to it. |
Jan 4 |
reviewed | Leave Closed The biquadratic character of $2$ mod $p$ for a prime of the form $p=4n+1$ |
Jan 3 |
reviewed | No Action Needed When does a ring surjection imply a surjection of the group of units? |
Jan 3 |
reviewed | Reject A Game of Knights and Queens |
Jan 3 |
comment |
Floors of rationals to powers: Infinite number of primes?
@GilKalai: Piatetski-Shapiro showed that if $1<r<c$ for a constant $c$ quite close to $1$ then $[n^r]$ takes on infinitely many primes (he gave an asymptotic formula for the number of such primes). The permissible value of $c$ has been increased subsequently by many authors. |
Jan 3 |
reviewed | Leave Closed On an asymptotic in Sarnak's book: “Some applications of modular forms” |
Jan 3 |
reviewed | Reject Useless math that became useful |
Jan 3 |
reviewed | Leave Open How many types of jigsaw puzzle pieces in n dimensions? |
Jan 2 |
reviewed | Approve Convergence of the empirical distribution function |
Jan 2 |
comment |
On an asymptotic in Sarnak's book: “Some applications of modular forms”
Keep in mind that $|\sin z|$ can get large if $z =x+iy$ is complex (as large as $e^{|y|}$). So if any of the $\theta_j$ are complex, you can find values of $k$ for which the LHS grows exponentially in $k$ (this is obvious if there is a single $\theta_j$ whose imaginary part is largest, and you'll need some argument if there are several with the same largest imaginary part). Hope that helps. |
Jan 2 |
comment |
Determinant and eigenvalues of a specific matrix
It's an example of a Toeplitz matrix. The entries are Gaussian. So I googled Gaussian Toeplitz matrix which gave the following paper sciencedirect.com/science/article/pii/0024379592902559 , which should answer your question. (I haven't read the paper myself so can't say for sure.) |
Jan 2 |
revised |
Relating the roots of polynomials to the solution sets of certain functional equations
Added tags |
Jan 1 |
reviewed | Leave Open A conjecture on solvablity of finite groups |
Jan 1 |
reviewed | No Action Needed Why should I care about topological modular forms? |
Jan 1 |
reviewed | Leave Open f(2013) = 2014? |
Dec 31 |
reviewed | Leave Open Find functions such that f(f(x))=f(x)e^x |
Dec 31 |
reviewed | No Action Needed Integrality of normalised L-values |