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Results tagged with zeta-functions
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user 49208
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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A (likely) positivity property of the Lerch zeta-function
From Prudnikov,Brychkov,Marichev Integral and Series, Vol.1, sect. 5.4.3, formula 1 we derive that
$$
\sum_{k=0}^\infty \frac{\cos(ak)}{(k+1/2)^{p+1}}=
\frac{1}{\Gamma(s)}\int_0^{\infty}\frac{t^p e^{- …
- 1,560