Difference between revisions of "Absolute convergence of secant zeta function"
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==Theorem== | ==Theorem== | ||
| − | The series $\psi_s(z)$ converges absolutely in the following cases: | + | The series defining the [[secant zeta function]] $\psi_s(z)$ converges absolutely in the following cases: |
# when $z=\dfrac{p}{q}$ with $q$ odd, $s>1$ | # when $z=\dfrac{p}{q}$ with $q$ odd, $s>1$ | ||
# when $z$ [[algebraic number| algebraic]] [[irrational number]] and $s >2$ | # when $z$ [[algebraic number| algebraic]] [[irrational number]] and $s >2$ | ||
Latest revision as of 06:09, 16 June 2016
Theorem
The series defining the secant zeta function $\psi_s(z)$ converges absolutely in the following cases:
- when $z=\dfrac{p}{q}$ with $q$ odd, $s>1$
- when $z$ algebraic irrational number and $s >2$
- when $z$ is algebraic irrational and $s=2$.
Proof
References
- Matilde Lalín: Secant zeta functions (2014): Theorem 1.
