MathOverflow

Littlewood conjectured that the gaps between the ordinates of successive complex zeros in $\zeta(s)$, tend to zero. Let's call this the Littlewood hypothesis(LH). Note that, as mentioned in the comments section, this is not actually a conjecture, but...

What function generates these indifference curves:
I want to generate graphs like this in Inkscape using its support for Python.
They have a few desired/required properties:

I want to know if there exists a closed formula for sum $A_n(X)=\sum \limits_{i=0}^n X^{i^2}$.
I have found if $n$ is odd then $(X^n+1)\text{ | } A_n(X)$, but I don't have found a closed formula.

Suppose I have a set whose cardinality is a power of 2, i.e. made of $N=2^n$ elements. If we consider the group of all the permutations of this set (the symmetric group $S_N$), we can say that it has $(2^n)!$ elements.Now suppose I define a family of...