Se p 19 96 Dynamical Zeta Functions , Nielsen Theory
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A Functional Equation for the Lefschetz Zeta Functions of Infinite Cyclic Coverings with an Application to Knot Theory
The Weil conjecture is a delightful theorem for algebraic varieties on finite fields and an important model for dynamical zeta functions. In this paper, we prove a functional equation of Lefschetz zeta functions for infinite cyclic coverings which is analogous to the Weil conjecture. Applying this functional equation to knot theory, we obtain a new view point on the reciprocity of the Alexander...
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C ertain generating functions—encoding properties of objects like prime numbers, periodic orbits, ...—have received the name of zeta functions. They are useful in studying the statistical properties of the objects in question. Zeta functions have generally been associated with problems of arithmetic or algebra and tend to have common features: meromorphy, Euler product formula, functional equat...
متن کاملA New Determinant for Quantum Chaos
Dynamical zeta functions [1], Fredholm determinants [2] and quantum Selberg zeta functions [3, 4] have recently been established as powerful tools for evaluation of classical and quantum averages in low dimensional chaotic dynamical systems [5] [8]. The convergence of cycle expansions [9] of zeta functions and Fredholm determinants depends on their analytic properties; particularly strong resul...
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This note is for an introduction to the validated numerics study of values of zeta and L functions. The subject matter of this talk lies in the area between Analysis, Algebra and Validated Numerics [1, 7].More specifically, I want to discuss the relations between the algebra and analysis of zeta and L functions and the evaluation of values of the functions. The talk is on some observations and ...
متن کاملA 11 Integers 11 B ( 2011 ) Dynamical Zeta Functions
These notes are a rather subjective account of the theory of dynamical zeta functions. They correspond to three lectures presented by the author at the “Numeration” meeting in Leiden in 2010. 1 A Selection of Zeta Functions In its various manifestations, a zeta function ζ(s) is usually a function of a complex variable s ∈ C. We will concentrate on three main types of zeta function, arising in t...
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