                          ! " Rosario Turco, Maria Colonnese, Michele Nardelli 1,2 1 Dipartimento di Scienze della Terra Università degli Studi di Napoli Federico II, Largo S. Marcellino, 10 80138 Napoli, Italy 2 Dipartimento di Matematica ed Applicazioni “R. Caccioppoli” Università degli Studi di Napoli “Federico II” – Polo delle Scienze e delle Tecnologie Monte S. Angelo, Via Cintia (Fuorigrotta), 80126 Napoli, Italy Abstract In this work the authors reproduce and deepen the themes of RH already presented in [25] [26], explaining formulas and showing different "special features" that are usually introduced with the theorem of prime numbers and useful to investigate further ways. One of the major results of this paper, through all the steps outlined, is that the conjecture on zeros of the Riemann’s zeta is true and demonstrable with some analytical steps and a theoretical remark (see. [30]). In the Chapter 1 (Remark A) and in the conclusion of Chapter 3 (Remark B), we have described the mathematical aspects concerning the proof of the conjecture “The nontrivial zeros of Riemann’s zeta have all multiplicity 1”. In the Chapter 2, we have described why ψ(x) is an equivalent RH. In the Chapter 3, we have described the mathematical aspects concerning the “Theorem free Region from nontrivial zeros”. In the Chapter 4, we have described also some mathematical arguments concerning the zeta strings and the p-adic and adelic strings. In conclusion, in the Chapter 5, we have showed the possible mathematical connections between some equations regarding the Chapter 4 and some equations of the Riemann Hypothesis here presented. The authors thank all readers, if they will return a feedback on this paper.