Partial Sums of the Series for the Dirichlet Eta Function, their Peculiar Convergence, the Simple Zeros Conjecture, and the RH

Luca Ghislanzoni

For any $s\in \mathbb{C}$ with $\Re (s)>0$, denote by ${\eta }_{n-1}(s)$ the $(n-1{)}^{th}$ partial sum of the Dirichlet series for the eta function $\eta (s)=1-2^{-s}+3^{-s}-\cdots$, and b…