Analytical research on the theory of prime numbers. (Recherches analytiques sur la théorie des nombres premiers.) (French) JFM 27.0155.03

de la Vallée Poussin, Ch. J.

Brux. S. sc. 21 B, 183-256, 281-362, 363-397 (1896).

Siehe JFM 27.0155.05.

MSC:

11M06	\(\zeta (s)\) and \(L(s, \chi)\)
11M20	Real zeros of \(L(s, \chi)\); results on \(L(1, \chi)\)
11M26	Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11N05	Distribution of primes
11N13	Primes in congruence classes
11N32	Primes represented by polynomials; other multiplicative structures of polynomial values

JFM Section:

Dritter Abschnitt. Niedere und höhere Arithmetik. Kapitel 2. Zahlentheorie. A. Allgemeines.

Keywords:

prime numbers; prime number theorem; Riemann’s zeta-function; \(L\)-functions; primes in progressions; primes in quadratic forms

Citations:

JFM 27.0155.05