MathOverflow

TL;DR: I would like to find an asymptotic for$$\sum_{n=2}^\infty \left(\log\left|1 - \frac z{a_n}\right| + \Re\left(\frac z{a_n}\right)\right), \tag{$*$}$$as $z\to \infty e^{i\theta}$, where $a_n = -n/\log n$.
Context: The reason is I asked whether there existed an entire function of order 1 such that the indicator$$h_f(\theta) := \limsup_{r\to\infty} \frac{\log |f(re^{i\theta})|}{r}$$satisfies$$\tag{1}h_f(\theta) = \begin{cases} \infty, \text{ if } |\theta...

Let $A/k$ be an abelian variety over a characteristic $p>0$ perfect field $k$. Usually, we say $A$ admits a lift to $W_2(k)$ if there exists an abelian scheme $\mathcal{A}/W_2(k)$ such that $\mathcal{A}\times_{W_2(k)}k\cong A$. However, by Serre...

Define: $X=\operatorname {Frege} (A) \iff \\ X= \{ y \mid \exists z: y= \{ a \subseteq A \mid a\text { is bijective to } z \}\}$
So $\operatorname {Frege}(X)$ is the set of all nonempty equivalence classes of subsets of $X$ under equivalence relation "bijection"....

Let $k$ be a field. Is it possible to characterize when a commutative $k[\varepsilon]$-algebra (where $k[\varepsilon] :\cong k[x]/x^2$) which is finite-dimensional over $k$ embeds into $M_n(k[\epsilon])$ as a $k[\varepsilon]$-subalgebra for some $n$...