Hilbert's eighth problem
Appearance
Hilbert's eighth problem is one of
distribution of primes and generalizations of Riemann hypothesis to other rings where prime ideals
take the place of primes.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Riemann_zeta_function_absolute_value.png/250px-Riemann_zeta_function_absolute_value.png)
Subtopics
Riemann hypothesis and generalizations
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.
Goldbach conjecture
He 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.
Twin prime conjecture
Generalized Riemann conjecture
Finally, he calls for mathematicians to generalize the ideas of the Riemann hypothesis to counting prime ideals in a number field.
External links
References
- Bombieri, Enrico (2006), "The Riemann Hypothesis", The Millennium Prize Problems, Clay Mathematics Institute Cambridge, MA: 107–124
- Moxley, Frederick (2021), "Complete solutions of inverse quantum orthogonal equivalence classes", Examples and Counterexamples, 1: 100003,
- ^ Bombieri (2006).
- ^ a b Moxley (2021).