All Questions

Voronin's Universality Theorem for $\zeta(s)$ is that the zeta function can uniformly approximate any non-vanishing holomorphic function to any degree of accuracy in the right-half of the critical ...

In [1] the authors provided a definition and characterization of turning points for the Riemann's zeta function. In this post I denote the Ramanujan's zeta function as $$\varphi(s)=\sum_{n=1}^\infty\...

In this post we consider the Ramanujan tau function $\tau(n)$, see the Wikipedia Ramanujan tau function, and we consider partial sums of its corresponding Dirichlet series (see for example the article ...

Suppose $(f_n(s))_n$ and $(g_n(s))_n$ are two sequences of Dirichlet series with positive coefficients such that $\exists \alpha\in\mathbb R$ such that for all $s\in\mathbb C$ with $\Re(s)>\alpha$ ...

Let $f(s)=\sum_n a_n n^{-s}$ be a Dirichlet series whose coefficients satisfy $\lvert a_n\rvert\leq n^{C}$. Then $f(s)$ converges absolutely in some halfplanes, and is conditionally convergent in (...