Ruelle type L-functions for torsion free abelian groups and associated arithmetic functions
山崎, 義徳 Ruelle type L-functions for torsion free abelian groups and associated arithmetic functions. In: 表現論シンポジウム, 2005/11/15-18, ヤマハリゾートつま恋.
15 November 2005: 表現論シンポジウム
We introduce Ruelle type L-functions attached to a character for a torsion free abelian group Γ of rank ν\ge 2 defined via an Euler product. It is shown that if the character is trivial, the imaginary axis is a natural boundary of this function when ν = 2, 4 or 8. We also study an arithmetic function which is naturally arising from the analysis of the L-functions.