Titlebook: Steps into Analytic Number Theory; A Problem-Based Intr Paul Pollack,Akash Singha Roy Textbook 2021 The Editor(s) (if applicable) and The A

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,Special Step A: Dirichlet’s Theorem for , = 8Carl Gustav Jacob Jacobi,how, by Dirichlet’s method, that there are infinitely many primes in each of the residue classes 1 mod  8, 3 mod  8, 5 mod  8, and 7 mod  8. This proof of Dirichlet’s theorem for . = 8 occupies a middle ground between the relatively simple arguments of Step #8 for the cases . = 3 and . = 4, and the

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Textbook 2021udents to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China.. . While it is recommended that the reader has a solid background in mathematical problem solving

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,Special Step A: Dirichlet’s Theorem for , = 8Carl Gustav Jacob Jacobi,f of Dirichlet’s theorem for . = 8 occupies a middle ground between the relatively simple arguments of Step #8 for the cases . = 3 and . = 4, and the more intricate arguments of the next two Special Steps, where Dirichlet’s theorem is proved in general.