Is there a proof of dirichlets theorem that does not require complex analysis?
Dirichlets theorem on primes
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analytic-number-theory
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1I don't know, but I can't see how to dispose of Dirichlet (complex) characters...Besides this, complex analysis is very beautiful and useful stuff, and Dirichlet's Theorem's proof is very nice...with complex analysis. – 2012-12-16
1 Answers
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The proof given in A Classical Introduction to Modern Number Theory by Ireland and Rosen doesn't use anything you wouldn't learn outside of say a basic calculus course.
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0Its a copyrighted book, so I believe an online copy of the book is illegal. However, you can buy a copy here : http://www.amazon.com/Classical-Introduction-Modern-Graduate-Mathematics/dp/038797329X. You can probably borrow this book from a local university's library, I'd be very surprised if the library lacked a book as famous as this. – 2012-12-16