ABC Conjecture and Riemann Hypothesis

In this paper, we consider two great unproven problems in mathematics in the language of inequalities; ABC conjecture and Riemann hypothesis. It is shown that the Riemann hypothesis is true in some initial cases. Then we study radical function, which is contained in the heart of ABC conjecture; we find an upper bound for it by assuming Riemann hypothesis and finally by using this bound, we combine Riemann hypothesis and ABC conjecture