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On the Hurwitz-type zeta function associated to the Lucas sequence
We study the theta function and the Hurwitz-type zeta function associated to
the Lucas sequence of the first kind determined by
the real numbers under certain natural assumptions on and . We
deduce an asymptotic expansion of the theta function as
and use it to obtain a meromorphic continuation of the
Hurwitz-type zeta function to the whole complex
plane. Moreover, we identify the residues of
at all poles in the half-plane