Tagged Questions
1
vote
1answer
63 views
What does this limit indicate?
$$\lim_{x\rightarrow\infty} \zeta(x)-\zeta(x)^{-1}-\zeta(x)^2 = -1$$
What does this limit indicate?
2
votes
1answer
146 views
Limit of the function $\zeta(x)/\zeta(x+1)$ as $x \to \infty$
I am looking for a simple proof that $\zeta(\alpha)/\zeta(\alpha+1) \to 1$ as $\alpha \to \infty$ (where $\zeta(\alpha)$ denotes the Riemann zeta function, $\zeta(\alpha) = \sum \limits_{n\geq 1} ...
2
votes
1answer
157 views
Why does $\frac{s}{s-1} > \zeta(s) > \frac{1}{s-1}$ imply $\lim_{s \to 1^{+}}(s-1)\zeta(s)=1$?
I am reading the paper Dirichlet's theorem: a real variable approach by Robin Chapman. In this paper, he constructs a proof via real analysis rather than complex analysis that $\zeta(s)$ is convergent ...
5
votes
3answers
279 views
Limit of Zeta function
I'm looking for a reference for (or an elementary proof of)
$$ \lim_{s \rightarrow 1} \left( \zeta(s) - \frac{1}{s-1} \right) = \gamma$$
Thanks for your help.
