(untitled) (European Journal of Pure and Applied Mathematics, 2025)
During the third decade of the last century, Arne Beurling introduced the generalise primes as any increasing positive real sequence starting with a real number greater than 1 called ”Beurling primes”. Where the fundamental theorem of arithmetics gives Beurling integers. This work study Beurling’s prime systems and concentrates on the upper bound of Beurling zeta function in the region (0, 1). This reflects of course on the size of the error term of Beurling counting function of integers Np(x).