The concept of "character" in Dirichlet's theorem on primes in an   arithmetic progression
  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 towards understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method. 
Jeremy Avigad and Rebecca Morris
math.HO