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

Peter Gustav Lejeune Dirichlet

arxiv: 0808.1408 · v2 · pith:C3YF3QZSnew · submitted 2008-08-10 · 🧮 math.HO · math.NT

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

Peter Gustav Lejeune Dirichlet This is my paper

classification 🧮 math.HO math.NT

keywords firstarithmeticdirichletinfinitelymanyprimesprogressionsanalytic

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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.

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