A Further Restricting the Gap Between (N_z-τx) and (N-τx) on R.H. By Using The Sense of ω-numbers and ωp-numbers

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Sarah Shakir Hasan,Faez Al-Maamori,LAbdulrahman H. Majeed

Abstract

In this article we use the sense of ω-numbers and ωp-numbers for restricting the gap between the error terms of Ω-results for 〖(N〗_z-τx) and the error terms of O-results for (N-τx) on Riemann Hypothesis (the Ω- results are generalized Ω-results for N_p as counting function of Beurling). The aim for this purpose we define: ℱ(􀝔) = 􀷍 􀟤(􀝉) 􀵬􀝂􀝈􀝋􀝓 􀵬􀝁 􀱢􀱥􀱝 􀳣 􀳘 􀵰 − 1􀵰 􀯠􀮹􀬵 Here F(x) could be use for building a ω-numbers and ωp-numbers from a positive real number x for two aims. The first one used for showing some of the behaviors of the error term of the function N(x) while the second one is used for preparing a secure code for any security algorithm.

Volume 11 | 05-Special Issue

Pages: 2043-2051

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