On Perron’s Formula and the Prime Numbers  

作　　者：Michael M. Anthony Michael M. Anthony(Department of Engineering, Enertron Inc., Hohenwald, Tennessee, USA)

机构地区：[1]Department of Engineering, Enertron Inc., Hohenwald, Tennessee, USA

出　　处：《Advances in Pure Mathematics》2024年第6期487-494,共8页理论数学进展（英文）

摘　　要：The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.

关 键 词：Perron Fixed Points ITERATIONS Number Theory Riemann Hypothesis ITERATIONS INVARIANCE PRIMES 

分 类 号：O17[理学—数学]