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Research output: Working paper › Research

**Mayer Transfer Operator Approach to Selberg Zeta Function.** / Momeni, Arash; Venkov, Alexei.

Research output: Working paper › Research

Momeni, A & Venkov, A 2010 'Mayer Transfer Operator Approach to Selberg Zeta Function' arXiv.org, pp. arXiv:1008.4229v2.

Momeni, A., & Venkov, A. (2010). *Mayer Transfer Operator Approach to Selberg Zeta Function*. (pp. arXiv:1008.4229v2). arXiv.org.

Momeni A, Venkov A. 2010. Mayer Transfer Operator Approach to Selberg Zeta Function. arXiv.org. pp. arXiv:1008.4229v2.

Momeni, Arash and Alexei Venkov *Mayer Transfer Operator Approach to Selberg Zeta Function*. arXiv:1008.4229v2. arXiv.org. 2010, 29 p.

Momeni A, Venkov A. Mayer Transfer Operator Approach to Selberg Zeta Function. arXiv.org. 2010, p. arXiv:1008.4229v2.

Momeni, Arash ; Venkov, Alexei. / **Mayer Transfer Operator Approach to Selberg Zeta Function**. arXiv.org, 2010. pp. arXiv:1008.4229v2

@techreport{654577e0e80b11dfa891000ea68e967b,

title = "Mayer Transfer Operator Approach to Selberg Zeta Function",

abstract = "These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function.",

keywords = "math-ph, math.MP, Mathematical Physics",

author = "Arash Momeni and Alexei Venkov",

note = "The proofs of Lemmas 1, 4, 5, Remark. 1 and section. 2.1 are corrected and modified; added reference (18) for section 2",

year = "2010",

language = "English",

pages = "arXiv:1008.4229v2",

publisher = "arXiv.org",

type = "WorkingPaper",

institution = "arXiv.org",

}

TY - UNPB

T1 - Mayer Transfer Operator Approach to Selberg Zeta Function

AU - Momeni, Arash

AU - Venkov, Alexei

N1 - The proofs of Lemmas 1, 4, 5, Remark. 1 and section. 2.1 are corrected and modified; added reference (18) for section 2

PY - 2010

Y1 - 2010

N2 - These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function.

AB - These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function.

KW - math-ph

KW - math.MP

KW - Mathematical Physics

M3 - Working paper

SP - arXiv:1008.4229v2

BT - Mayer Transfer Operator Approach to Selberg Zeta Function

PB - arXiv.org

ER -