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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*Hurwitz Zeta is a sum of Dirichlet L Functions, and vice-versa*
Friday, Feb 8 2013

Expository and Math.NT and Mathematics character, dirichlet, hurwitz zeta, l function, math, mathematics, number theory 7:31 pm

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*An Application of Mobius Inversion to Certain Asymptotics I*
Thursday, Nov 8 2012

Expository and Math.NT and Mathematics asymptotics, David Lowry, dirichlet, math, mathematics, mobius inversion, number theory, research, zeta function 2:23 pm

In this note, I consider an application of generalized Mobius Inversion to extract information of arithmetical sums with asymptotics of the form for a fixed and a constant , so that the sum is over both and . We will see that .