Dirichlets 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 Eulers earlier work on the zeta functi
on 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.
In this short note we give an expression for some numbers $n$ such that the polynomial $x^{2p}-nx^p+1$ is reducible.
Felix Kleins so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The given translati
on was made in 1892 by Dr. M. W. Haskell and transcribed by N. C. Rughoonauth. We replaced bibliographical data in text and footnotes with pointers to a complete bibliography section.
Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelles Journal (1829) with numerous typographical corrections, and added a completed bibliography. Dirichlet
prouve la convergence generale de la series de Fourier, apr`es avoir montre des erreurs dans un essai par Cauchy. Nous avons transcrit de Crelles journal (1829) avec de nombreuses corrections typographiques, et avons ajoute une bibliographie compl`ete.
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear recurrence
s tries to fill a gap in the literature by giving many extensive examples.
