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Characterization of turning points for the Ramanujan's zeta function in the spirit of a definition by Arias de Reyna and van de Lune
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\...
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Zeros of partial sums of the Ramanujan's zeta function
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 ...
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Special values of Hecke L-function
The Dedekind zeta function for a number field $K$ is defined as
$\zeta_K(s)=\sum_{I\subset O_K} (N_{K/\mathbb{Q}}(I))^{-s}$.
By attaching a Hecke character $\psi$, we can define $L(s,\psi)=\sum_{I\...