Studying the upper bound of Beurling zeta function in the strip (0,1)

Alzahra, Safa Mohsen Abd; Al-Maamori, Faez A.

doi:10.47974/JIM-1913

Open Access Research Article

Studying the upper bound of Beurling zeta function in the strip (0,1)

^*Safa Mohsen Abd AlzahraCorresponding authorsafa.alzahra.pure440@student.uobylon.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of BabylonBabylon, IraqView full profile → , Faez A. Al-Maamorifaez@itnetuobabylon.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of BabylonDepartment of Security College of Information Technology University of BabylonBabylon, IraqView full profile →

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pp. 933–938Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1913XML

Received:: 06 Mar 2024
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1913
Pages:: 933–938

Abstract

During the third decade of the last century, Arne Beurling stated the sense of the generalized prim systems. He said that any positive, increasingly real sequence started from any number greater than one precisely, and this sequence is called Beurling primes (or the generalized prim). They also mentioned that the fundamental Theorem of arithmetic gives the generalized integers. In the seventeenth decade of the last century, Diamond modified all the related counted functions of prime πg (x) and integers Ng (x) and the generalized Riemann zeta function. This work addresses an overview of the behavior of the generalized counting function Ng (x) where the change happens in the error term of Ng (x). The changing in E(x) = |Ng (x)-ρx| implies changing in the real part of (s = σ + it) and hence affects the behavior of the generalized ζg (x).

Keywords

A N T Beurling’s primes

Subject Classifications

26A4530B30

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