The Riemann zeta function is important in number theory. In particular, the Riemann hypothesis, one of the seven Millenium Prize Problems, states that the non-trivial zeros of the zeta function all have real part equal to 1/2. The truth of the Riemann hypothesis has consequences for the distribution of prime numbers.
This problem deals only with values of the zeta function for real arguments greater than 1. For a positive integer argument 
the zeta function is the sum of the reciprocals of integers raised to the power of x. Euler showed that when x is an even integer, the value of the zeta function is proportional to 
, and Cody Problem 45939 uses this fact to estimate π. Less is known about the zeta function for odd integer arguments, but Apery proved that 
, now known as Apery's constant, is irrational.
the zeta function is the sum of the reciprocals of integers raised to the power of x. Euler showed that when x is an even integer, the value of the zeta function is proportional to , and Cody Problem 45939 uses this fact to estimate π. Less is known about the zeta function for odd integer arguments, but Apery proved that , now known as Apery's constant, is irrational.Evaluate the zeta function for real arguments greater than 1.
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