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
Keyword(s):  
Zeta Function ◽  
Distribution Of Zeros ◽  
Ruelle Zeta Function

scholarly journals Ruelle Zeta Function from Field Theory

2020 ◽  
Vol 21 (12) ◽  
pp. 3835-3867
Author(s):  
Charles Hadfield ◽  
Santosh Kandel ◽  
Michele Schiavina
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Lagrangian Submanifolds ◽  
Analytic Torsion ◽  
Contact Manifolds ◽  
Gauge Fixing ◽  
Ruelle Zeta Function

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.

scholarly journals Investigation of a Control Function Determining the Location of the Zeros as a Possible Proof of the Riemann Hypothesis.

2022 ◽  
Author(s):  
Miroslav Sukenik
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Riemann Hypothesis ◽  
Control Function ◽  
Distribution Of Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Zero Points

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.

scholarly journals On the distribution of zeros of the Hurwitz zeta-function

2007 ◽  
Vol 76 (257) ◽  
pp. 323-338 ◽  
Author(s):  
Ramūnas Garunkštis ◽  
Jörn Steuding
Keyword(s):  
Zeta Function ◽  
Hurwitz Zeta Function ◽  
Distribution Of Zeros

scholarly journals Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps

2007 ◽  
Vol 59 (2) ◽  
pp. 311-331 ◽  
Author(s):  
Hans Christianson
Keyword(s):  
Dynamical System ◽  
Lower Bound ◽  
Zeta Function ◽  
Julia Set ◽  
Upper Bounds ◽  
Rational Maps ◽  
Rational Map ◽  
Numerical Work ◽  
Number Of Zeros ◽  
Ruelle Zeta Function

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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