Ellison, William John; Mendès France, Michel Les nombres premiers. (French) Zbl 0313.10001 Publication de l’Institut de Mathématique de l’Université de Nancago. IX. Actualités scientifiques et industrielles. 1366. Paris: Hermann, éditeurs. xiv, 442 p. F 118.00 (1975). Reviewer: François Fricker Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 47 Documents MSC: 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11N05 Distribution of primes 11N13 Primes in congruence classes 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses 11L03 Trigonometric and exponential sums (general theory) 11L07 Estimates on exponential sums 11L15 Weyl sums 11N37 Asymptotic results on arithmetic functions 11N80 Generalized primes and integers 11P32 Goldbach-type theorems; other additive questions involving primes 11K06 General theory of distribution modulo \(1\) Keywords:Chebyshev theorems; prime number theorem; elementary proof; arithmetic progressions; Riemann zeta-function; Riemann hypothesis; irregularities in the distribution of prime numbers; Dirichlet \(L\)-series; sums of prime numbers; trigonometric sums PDF BibTeX XML OpenURL