## Hurwitz Zeta is a sum of Dirichlet L Functions, and vice-versa

At least three times now, I have needed to use that Hurwitz Zeta functions are a sum of L-functions and its converse, only to have forgotten how it goes. And unfortunately, the current wikipedia article on the Hurwitz Zeta function has a mistake, omitting the $varphi$ term (although it will soon be corrected). Instead of re-doing it each time, I write this detail here, below the fold.

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Posted in Expository, Math.NT, Mathematics
Tagged character, dirichlet, hurwitz zeta, l function, math, mathematics, number theory
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