Is the Riemann hypothesis still unsolved?
Is the Riemann hypothesis still unsolved?
The 160-year-old Riemann hypothesis has deep connections to the distribution of prime numbers and remains one of the most important unsolved problems in mathematics. If proved, it would immediately solve many other open problems in number theory and refine our understanding of the behavior of prime numbers.
What is the application of Riemann hypothesis?
Riemann Hypothesis is one of the most important unresolved conjectures in mathematics. It connects the distribution of prime numbers with zeroes of Zeta function, defined on the complex plane. A number of algorithms in algebra and number theory rely on the correctness of Riemann Hypothesis or its generalizations.
When did Bernhard Riemann propose the Riemann hypothesis?
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 12. It was proposed by Bernhard Riemann (1859), after whom it is named.
Is the Riemann hypothesis in the singular case?
In the nonsingular case the Riemann hypothesis is a consequence of the maximal accretive property of a Radon transformation defined in Fourier analysis. In the singular case the Riemann hypothesis is a consequence of the maximal accretive property of the restriction of the Radon transformation to a subspace defined by parity.
How did Deligne prove the Riemann hypothesis over finite fields?
Multiple zeta functions. Deligne’s proof of the Riemann hypothesis over finite fields used the zeta functions of product varieties, whose zeros and poles correspond to sums of zeros and poles of the original zeta function, in order to bound the real parts of the zeros of the original zeta function.
Are there any zeta functions that have a Riemann hypothesis?
Other zeta functions. Goss zeta functions of function fields have a Riemann hypothesis, proved by Sheats (1998). The main conjecture of Iwasawa theory, proved by Barry Mazur and Andrew Wiles for cyclotomic fields, and Wiles for totally real fields, identifies the zeros of a p -adic L -function with the eigenvalues of an operator,…