Hilbert's eighth problem

Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900.

Hilbert calls for a solution to the Riemann hypothesis, which has long been regarded as the deepest open problem in mathematics.

Given the solution,[2] he calls for more thorough investigation into Riemann's zeta function and the prime number theorem.

Hilbert calls for a solution to the Goldbach conjecture, as well as more general problems, such as finding infinitely many pairs of primes solving a fixed linear diophantine equation.

Finally, Hilbert calls for mathematicians to generalize the ideas of the Riemann hypothesis to counting prime ideals in a number field.

Absolute value of the ζ-function. Hilbert's eighth problem includes the Riemann hypothesis , which states that this function can only have non-trivial zeroes along the line x = 1/2 [ 2 ] .