state the Riemann hypothesis

The Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function (a complex function defined for complex numbers) have a real part equal to 1/2. In other words, if a non-trivial zero of the zeta function is denoted as s = a + bi (where a and b are real numbers and i is the imaginary unit), then the Riemann hypothesis asserts that a = 1/2 for all such zeros. The Riemann hypothesis is one of the most famous unsolved problems in mathematics and has implications for the distribution of prime numbers.