Higher dimension: the prime number theorem and the Chebotarev density theorem

2016 ◽  
pp. 141-156
Keyword(s):  
Prime Number ◽  
Prime Number Theorem ◽  
Density Theorem ◽  
Higher Dimension ◽  
Chebotarev Density Theorem

scholarly journals Bowen's equidistribution theory and the Dirichlet density theorem

1984 ◽  
Vol 4 (1) ◽  
pp. 117-134 ◽  
Author(s):  
William Parry
Keyword(s):  
Asymptotic Formula ◽  
Prime Number ◽  
Zeta Functions ◽  
Prime Number Theorem ◽  
Density Theorem ◽  
Analytic Extension ◽  
Closed Orbits ◽  
Basic Set ◽  
Dirichlet Density ◽  
Extension Result

AbstractLet φ be an Axiom A flow restricted to a basic set, let g be a C∞ function and let , where λg(τ) is the g length of the closest orbit τ, λ(τ) is the period of τ and h is the topological entropy of φ. We obtain an asymptotic formula for πg which includes the ‘prime number’ theorem for closed orbits. This result generalizes Bowen's theorem on the equidistribution of closed orbits. After establishing an analytic extension result for certain zeta functions the proofs proceed by orthodox number theoretical techniques.

scholarly journals Sign changes in the prime number theorem

2021 ◽  
Author(s):  
Thomas Morrill ◽  
Dave Platt ◽  
Tim Trudgian
Keyword(s):  
Prime Number ◽  
Prime Number Theorem ◽  
Sign Changes

scholarly journals The prime number theorem is PRA-provable

2001 ◽  
Vol 257 (1-2) ◽  
pp. 185-239 ◽  
Author(s):  
Olivier Sudac
Keyword(s):  
Prime Number ◽  
Prime Number Theorem

The Prime Number Theorem

2016 ◽  
pp. 47-50
Author(s):  
Barry Mazur ◽  
William Stein
Keyword(s):  
Prime Number ◽  
Prime Number Theorem
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