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One and a half century of research on Riemann hypothesis. (Un siècle et demi de recherches sur l’hypothèse de Riemann.) (French) Zbl 1298.11087
This is an expert overview article on the Riemann hypothesis, probably the most important open problem in mathematics. Enunciated by B. Riemann in 1859, the Riemann hypothesis is the statement that all complex non-trivial zeros of the Riemann zeta-function \(\zeta(s)\) have real part equal to 1/2. The author presents much of the history of the subject, and gives 19 equivalent assertions of the Riemann hypothesis. There are 59 references at the end of the paper, which cover much of the work involving the Riemann hypothesis. This paper will be of interest both to novices and experts.
MSC:
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11-03 History of number theory
01A60 History of mathematics in the 20th century
01A55 History of mathematics in the 19th century
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