The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression |
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Authors: | Jeremy Avigad Rebecca Morris |
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Institution: | 1. Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, USA 2. Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA
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Abstract: | In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses of Dirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method. |
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