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The Riemann zeta function is defined for complex s with real part greater than 1 by the absolutely convergent infinite series ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 1 s + 1 2 s + 1 3 s + ⋯
It is of great interest in number theory because it implies results about the distribution of prime numbers. Many consider it to be the most important unsolved problem in pure mathematics. In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1 / 2.