### Abstract

For a C-2 weak-mixing Axiom-A flow phi(t) : M -> M on a Riemannian manifold M and a basic set Lambda for phi(t), we consider the Ruelle transfer operator Lf-s tau+zg, where f and g are real-valued Holder functions on Lambda, tau is the roof function and s, z are complex parameters. Under some assumptions about phi(t) for arbitrary Holder f, g, we establish estimates for the iterations of this Ruelle operator when vertical bar lmz vertical bar 0, 0 <nu <1 (nu = 1 for Lipschitz f g), in the spirit of the estimates for operators with one complex parameter (see [2,11,12]). Applying these estimates, we obtain a non-zero analytic extension of the zeta function zeta(s, z) for P-f - epsilon <Re (s)

Original language | English |
---|---|

Pages (from-to) | 595-599 |

Number of pages | 5 |

Journal | Comptes rendus mathematique |

Volume | 353 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2015 |

### Fingerprint

### Cite this

*Comptes rendus mathematique*,

*353*(7), 595-599. https://doi.org/10.1016/j.crma.2015.04.005