Riemann hypothesis
Hipótesis de Riemann y fórmula explícita para los primos
- Date
- 1859 · confidence high
- Place
- Göttingen, Germany
- Credited to
- Bernhard Riemann (On the Number of Primes Less Than a Given Magnitude)
- People
- 👤 Bernhard Riemann1826–1866
- Field
- Knowledge & symbols
What was discovered
The extension of zeta to the complex plane, a functional equation and a formula expressing the count of primes in terms of the zeros of zeta; the conjecture that all non-trivial zeros have real part 1/2. It remains open and is the most important problem in mathematics.
It is Hilbert's eighth problem and one of the seven Millennium Problems; trillions of zeros have been verified numerically.
What it led to
- the prime number theorem
- analytic number theory
- Hilbert's problems and the Millennium Problems
- connections with random matrices and quantum physics
Built on
- Euler product and zeta function1737
- Complex analysis: Cauchy integral theorem and residues1825
- Cauchy's complex analysis
- Gauss and Legendre's conjecture on the density of primes