in analytic number theory
Five conjectures, formulated by B. Riemann (1876), concerning the distribution of the non-trivial zeros of the zeta-function , and the expression via these zeros of the number of prime numbers not exceeding a real number . One of the Riemann hypotheses has neither been proved nor disproved: All non-trivial zeros of the zeta-function lie on the straight line .
For the list of all 5 conjectures see Zeta-function.
|[a1]||A. Ivic, "The Riemann zeta-function" , Wiley (1985)|
|[a2]||E.C. Titchmarsh, "The theory of the Riemann zeta-function" , Clarendon Press (1951)|
|[a3]||H.M. Edwards, "Riemann's zeta function" , Acad. Press (1974) pp. Chapt. 3|
Riemann hypotheses. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Riemann_hypotheses&oldid=13088