MathOverflow

I am wondering whether there is an established precedent in analytic number theory for combining density-one arguments with global topological or geometric observables.
More specifically, suppose one has a family of arithmetic signals or oscillatory objects depending on a height parameter $T$, together with a cumulative quantity such as a winding number, winding index, phase accumulation, or another homotopy-type invariant...

Is it true that every holomorphic function in the unit disc is the sum of two non-vanishing holomorphic functions ?
The terminology is borrowed from this article.
The answer would be positive if given any sequence of points in the unit disc accumulating to the boundary $a_1,a_2...$ and multiplicites $m_1,m_2 ...$, I can construct a function $f\in \mathcal{O}(\mathbb{D})$ such that for every $i$ there exists $k...

It is well known that the ratio of the number of full reptend primes (FRPs) to the number of primes is equal to the Artin's constant. But has anyone observed that the ratio of the sum of reciprocals of FRPs and the sum of reciprocals of primes is close...

Let $X$ be a surface as in the title. Rick Miranda said that $X$ is a Steiner cubic in $\mathbb{P}^4$, and the cover map is projection. Invariants of $X$ can be computed directly, $p_g(X)=0,K^2_X=8,e(X)=4$.
My question is,
Question: What is a Steiner cubic? Why $X$ is a Steiner cubic?...