scholarly journals On the distribution of zeros of a Ruelle zeta-function

1994 ◽  
Vol 159 (3) ◽  
pp. 433-441 ◽  
Author(s):  
A. Eremenko ◽  
G. Levin ◽  
M. Sodin
2020 ◽  
Vol 21 (12) ◽  
pp. 3835-3867
Author(s):  
Charles Hadfield ◽  
Santosh Kandel ◽  
Michele Schiavina

Abstract We propose a field-theoretic interpretation of Ruelle zeta function and show how it can be seen as the partition function for BF theory when an unusual gauge-fixing condition on contact manifolds is imposed. This suggests an alternative rephrasing of a conjecture due to Fried on the equivalence between Ruelle zeta function and analytic torsion, in terms of homotopies of Lagrangian submanifolds.


2022 ◽  
Author(s):  
Miroslav Sukenik

The article examines the control function in relation to the distribution of Zeros on thecritical line x = 0,5. To confirm this hypothesis, it will be necessary to perform a large number ofstatistical analyzes of the distribution of non-trivial zero points of the Riemann Zeta function.


2007 ◽  
Vol 76 (257) ◽  
pp. 323-338 ◽  
Author(s):  
Ramūnas Garunkštis ◽  
Jörn Steuding

2007 ◽  
Vol 59 (2) ◽  
pp. 311-331 ◽  
Author(s):  
Hans Christianson

AbstractThis paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic rational map. It is shown that the zeta function is bounded by exp(CK|s|δ) in strips | Re s| ≤ K, where δ is the dimension of the Julia set. This leads to bounds on the number of zeros in strips (interpreted as the Pollicott–Ruelle resonances of this dynamical system). An upper bound on the number of zeros in polynomial regions {| Re s| ≤ | Im s|α} is given, followed by weaker lower bound estimates in strips {Re s > –C, | Ims| ≤ r}, and logarithmic neighbourhoods {| Re s| ≤ ρlog | Ims|}. Recent numerical work of Strain–Zworski suggests the upper bounds in strips are optimal.


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