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

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

2008-08-10

arxiv.org/abs/0808.1408v1

Mathematics

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22 pages

Scientific paper

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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