arXiv subjects

Peter Gustav Lejeune Dirichlet

Publications and source records attributed to Peter Gustav Lejeune Dirichlet.

2 recordsLinked to original sources

arXiv2014

There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime

Dirichlet's proof of infinitely many primes in arithmetic progressions was published in 1837, introduced L-series for the first time, and it is said to have started rigorous analytic number theory. Dirichlet uses Euler's earlier work on the zeta function and the distribution of primes. He first proves a simpler case before going to full generality. The paper was translated from German by R. Stephan and given a reference section.

math.HO↗

arXiv2008

Sur la convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données

Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelle's Journal (1829) with numerous typographical corrections, and added a completed bibliography. Dirichlet prouve la convergence générale de la séries de Fourier, après avoir montré des erreurs dans un essai par Cauchy. Nous avons transcrit de Crelle's journal (1829) avec de nombreuses corrections typographiques, et avons ajouté une bibliographie complète.

math.HO↗