Two New Equivalent Statements of Riemann Hypothesis
The distribution of such prime numbers among all natural numbersdoes not follow any regular pattern; however, the Germanmathematician G. F. B. Riemann (1826-1866) observed that thefrequency of prime numbers is very closely related to the behaviorof an elaborate function called the Riemann zeta function s. Thenontrivial zeroes of zeta function have 1 2 as their real part. This hasbeen checked for the first 1,500,000,000 solutions. A proof that it istrue for every interesting solution would shed light on many ofthe mysteries surrounding the distribution of prime numbers.The celebrated Riemann hypothesis remains unsolved since it wasintroduced in 1859. Miscellaneous approaches have been consideredwithout any exact and complete proof. Furthermore, some equivalentstatements have been established.In this work, we consider the famous Robin inequality and propound aconnection to the theory of univalent functions by the means of Koebefunction.