  Motivated by recent work of Deitmar-Koyama-Kurokawa, Kurokawa-Ochiai,
Connes-Consani, and the author, we define some multivariable deformed zeta
functions of Hurwitz-Igusa type for a Noetherian $\F_1$-scheme $X$ in the sense
of Connes-Consani.
  Our zeta functions generalize both the zeta functions studied by
Deitmar-Koyama-Kurokawa, Kurokawa-Ochiai, and the log derivative of the
modified Soul\'e type zeta function Connes-Consani.
  We give an explicit presentation for these zeta functions using the Hurwitz
zeta functions, and so, we can derive its meromorphicity.
  When restricted to the log derivative of the modified Soul\'e type zeta
functions, we find our invariant $\mu(A)$ for a finite abelian group $A$,
introduced in ArXiv-0907.0918v2, plays an extremely important role in the
Soul\'e type zeta functions.
