An Outer Generalized Prime System and Some Discrete Examples

Ahmed B. AL-Nafee^1*, Faez AL-Maamori²  

^1*Ministry of Education Open Educational College, Department of Mathematics, Babylon, Iraq.

²Department of computer science,Babylon University, Babylon, Iraq.

Emails: Ahm_math_88@yahoo.com; Faez352013@gmail.com

Abstract

Beurling (or generalized) prime system has been defined by Arne Beurling in 1937, and several couthers have been working on this during the last century. This work focuses on addressing some concrete examples of an outer generalized prime system involving Beurling zeta function. The core of this work is to create a discrete generalized prime system under a fixed condition to give a new upper bound for Beurling zeta function.

Keyword: Generalized Prime Systems; Beurling Zeta Function.