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

Meromorphicity of some deformed multivariable zeta functions for $F_1$-schemes