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It follows from a general theorem of Honda that the formal group with the logarithm $$ x+x^{2^s}/2+x^{3^s}/3+x^{4^s}/4+\cdots $$ has integer coefficients. I became interested in it because its $p$-typ …

On the OP request, here is the plot of first 10000 partial sums. Following Terry Tao's suggestion, here is the plot of ($n$th partial sum) $+2^{\frac32}/\sqrt{\pi n}$ for $n$ up to one million: …

Wow. This deserves a separate answer. As I mentioned in a comment, motivated by the question, in a previous comment, by Igor Rivin whether an efficient primality test can be made if the statement in …

Contemplating a question on math.SE, I have stumbled on this: Here, the point labeled $n$ is that root of the $n$th Bernoulli polynomial which has smallest positive imaginary part. Does anyone …

Just an illustration - for $m$ up to 6000, $r$ up to 120. Quite mysterious looking, I would say. Version 2: in the coordinate system suggested by the answer of Lucia it looks somehow more regular, …

This is an immediate successor of Chebyshev polynomials of the first kind and primality testing and does not have any other motivation - although original motivation seems to be huge since a positive …

This is another question about visualization of Ford circles, the previous one being Confusion with practically implementing rational approximations. Here is an output of zooming into Ford circles at …

The question is motivated by yet another possible approach to a combinatorial problem formulated previously in "Special" meanders. I'm not giving details of the connection as I believe the question is …

NOT AN ANSWER, just an illustration :D ($g$ up to $n=150$) Quite amusing... In case anybody wants to play with this, here is the Mathematica code g[n_] := Dot @@ Transpose[FactorInteger[n]] Graph …

At least some part of the features may be explained by plotting $\frac1{r(n)}$, it looks like this: It is more or less clear that the slopes are $\frac1{k^2}$, $k=1,2,3,...$ (So the original plot …

According to Wikipedia, examples of PIDs with nontrivial $SK_1$ have been first given by Ischebeck in "Hauptidealringe mit nichttrivialer $SK_1$-Gruppe" (Arch. Math. 35 (1980), 138–139) and by Grayson …

This question arose from the recent one, roots of a polynomial linked to mock theta function?. Let $$ g(x):=\sum_{k=0}^\infty x^k\prod_{j=1}^{k-1}(1 + x^j)^2\\=1+x+x^2+3 x^3+4 x^4+6 x^5+10 x^6+15 x^7+ …

The 26th power of the Dedekind $\eta$ function has been mentioned several times here on MO: A 14th and 26th-power Dedekind eta function identity? What's the status of the following relationship betwee …

This question is inspired by Why are Bessel function and Kloosterman sum similar? - it developed in me desire to understand Kloosterman sums better. There seems to be common knowledge that Gauss, Jac …

Whenever I encounter anything about modular parametrizations, I have a feeling it is something very unnatural: you have some kind of moduli space and all of a sudden it parametrizes an object represen …