Explicit formulas for the pair correlation of zeros of functions in the Selberg class

2002 ◽  
Vol 14 (1) ◽  
Author(s):  
Ram Murty ◽  
Alexandru Zaharescu
Keyword(s):  
Pair Correlation ◽  
Selberg Class ◽  
Explicit Formulas ◽  
Zeros Of Functions

scholarly journals Statistical Regularity of Apollonian Gaskets

2019 ◽  
Author(s):  
Xin Zhang
Keyword(s):  
Ergodic Theory ◽  
Nearest Neighbor ◽  
Pair Correlation ◽  
Hyperbolic Spaces ◽  
Infinite Volume ◽  
Statistical Regularity ◽  
Explicit Formulas ◽  
Convergence Of Moments

Abstract Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the limiting pair correlation and the limiting nearest neighbor spacing of centers of circles from a fixed Apollonian gasket. These are corollaries of the convergence of moments that we prove. The input from ergodic theory is an extension of Mohammadi–Oh’s theorem on the equidisribution of expanding horospheres in the frame fundles of infinite volume hyperbolic spaces.

scholarly journals On the zeros of functions in the Selberg class

2008 ◽  
Vol 38 (2) ◽  
pp. 121-130 ◽  
Author(s):  
Anirban Mukhopadhyay ◽  
Kotyada Srinivas ◽  
Krishnan Rajkumar
Keyword(s):  
Selberg Class ◽  
Zeros Of Functions

scholarly journals Distinct zeros of functions in the Selberg class

2002 ◽  
Vol 103 (3) ◽  
pp. 201-207 ◽  
Author(s):  
K. Srinivas
Keyword(s):  
Selberg Class ◽  
Zeros Of Functions
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