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Results tagged with zeta-functions
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user 536861
Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.
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Show that the function $(n+2)\zeta(n+3)-\zeta(n+2)-n-1$ is positive on $\mathbb{N}.$
I'm trying to prove the positivity of the function $(n+2)\zeta(n+3)-\zeta(n+2)-n-1$ on $\mathbb{N}$ using the inequalities
\begin{equation*}
\frac{s+1}{s}\zeta(s)\zeta(s+2)\geq \zeta^2(s+1),\quad s>1
…
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