All Questions

Let $\nu_2(a)$ be the $2$-adic valuation of an integer $x$, i.e. the largest power $t$ such that $2^t$ divides $x$. Define the operator $D=x\frac{d}{dx}$ and the polynomial $\Phi_k(x)=\frac{x^{k+1}-1}{...

Denote $\pmb{a}=(a_1,\dots,a_d)\in\mathbb{R}^d$ and consider the set $$\mathcal{E}_d=\{\pmb{a}\in\mathbb{R}^d: \text{each root $\xi$ of $x^d+a_dx^{d-1}+\cdots+a_2x+a_1=0$ lies in $\vert\xi\vert<1$}\...

The Series Consider the series identity $$\Phi(s) = \sum_{n=1}^\infty \frac{\mu(n) (\log n)^k}{n^s} \sum_{r \in R(n)} \zeta(s,r/n) = \sum_{n=1}^\infty \frac{\Lambda_k'(f(n))}{n^s}$$ $$R(n) = \left\...