Masanori Katsurada

On the Hurwitz—Lerch zeta-function

Summary. Let

Explicit Formulas and Asymptotic Expansions for Certain Mean Square of Hurwitz Zeta-Functions.

\Phi(z,s,\alpha) = \sum\limits^\infty_{n = 0} {z^n \over (n + \alpha)^s}

The mean values of Dirichlet

be the Hurwitz-Lerch zeta-function and

L

\phi(\xi,s,\alpha)=\Phi(e^{2\pi i\xi},s,\alpha)

-functions at integer points and class numbers of cyclotomic fields

for

Explicit Formulas and Asymptotic Expansions for Certain Mean Square of Hurwitz Zeta-Functions: III

\xi\in{\Bbb R}

Asymptotic expansions of the mean values of DirichletL-functions III

its uniformization.

Asymptotic expansions of the mean values of DirichletL-functions

\Phi(z,s,\alpha)

Power series and asymptotic series associated with the Lerch zeta-function

reduces to the usual Hurwitz zeta-function

An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions

\zeta(s,\alpha)