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ANALYTIC NUMBER THEORY AND DIRICHLET’S THEOREM

In this paper, we prove Dirichlet’s theorem that, given any pair h, k with (h, k) = 1, there are infinitely many prime numbers congruent to h (mod k). Although this theorem lies strictly within the realm of number theory, its proof employs a range of tools from other branches of mathematics, most notably characters from group theory and holomorphic functions from complex analysis.