Talk:Hurwitz zeta function

From Wikipedia, the free encyclopedia

[edit] Multiplication theorem

There is a useful generalization of the multiplication theorem for the Hurwitz zeta function. In Maple notation:

   sum(Zeta(s,a+p/q),p=1..q-1) = q^s*Zeta(s,q*a)

where (q-1) is a natural number. It reduces to the simpler form on writing a=1/q (and recalling that Zeta(s,1) is the Riemann zeta function). [The proof is trivial ...]

So put it into the article. The above equation in LaTeX is
\sum_{p=1}^{q-1}\zeta(s,a+p/q)=q^s\,\zeta(s,qa)

PAR 20:21, 3 August 2006 (UTC)

Sorry - I made an error. The lower bound of the sum (over p) should be zero, not unity! So -

\sum_{p=0}^{q-1}\zeta(s,a+p/q)=q^s\,\zeta(s,qa)

Hair Commodore 22:00, 30 October 2006 (UTC)

[edit] region of convergence

This topic is in need of attention from an expert on the subject.
The section or sections that need attention may be noted in a message below.

The series, and other formulas, should include a discussion of the regions of absolute and conditional convergence. I slapped an expert tag on the section introducing this idea. linas (talk) 20:36, 18 November 2007 (UTC)