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

@article{citeulike:3112182, abstract = {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.}, archivePrefix = {arXiv}, author = {Dirichlet, Peter G.}, citeulike-article-id = {3112182}, citeulike-linkout-0 = {http://arxiv.org/abs/0808.1408}, citeulike-linkout-1 = {http://arxiv.org/pdf/0808.1408}, day = {10}, eprint = {0808.1408}, keywords = {available-in-tex-format, historical-work, mathematics, number-theory, transcribed-by-rwst}, month = {Aug}, posted-at = {2008-08-12 17:00:10}, priority = {2}, title = {There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime}, url = {http://arxiv.org/abs/0808.1408}, year = {2008} }

TY - JOUR ID - citeulike:3112182 L3 - citeulike-article-id:3112182 N2 - 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. TI - There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime KW - available-in-tex-format KW - historical-work KW - mathematics KW - number-theory KW - transcribed-by-rwst AU - Dirichlet, Peter PY - 2008/Aug/10/ UR - http://arxiv.org/abs/0808.1408 ER -