The collected works, published 188997, of the great nineteenth-century German mathematician, Dirichlet, the founder of analytic number theory.Peter Dirichlet (180559) belonged to a network of influential French and German mathematicians, and his many achievements included foundational work in analytic number theory. These two volumes, which appeared in 188997, are a collection of all his published work, together with several unpublished papers and selected correspondence.Peter Dirichlet (180559) belonged to a network of influential French and German mathematicians, and his many achievements included foundational work in analytic number theory. These two volumes, which appeared in 188997, are a collection of all his published work, together with several unpublished papers and selected correspondence.The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (180559) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and G?ttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 188997, was compiled by Leopold Kronecker (182391). Volume 1 contains works published by Dirichlet up to 1843, together with a related 1846 essay.Vorwort; 1. M?moire sur l'impossibilit? de quelques ?quations ind?termin?es du cinqui?me degr?; 2. M?moire sur l'impossibilit? de quelques ?quations ind?termin?es du cinqui?me degr?; 3. De formis linearibus, in quibus continentur divisores primi quarumdam formularum graduum superiorum commentatio; 4. Recherches lcī