Dirichlet L-Series and Primes in an Arithmetic Progression

Abstract

Our principal goal in this chapter will be to prove the analogue of Dirichlet’s famous theorem about primes in arithmetic progressions. This was first proved by H. Kornblum in his PhD thesis written, just before the onset of World War I, under the direction of Edmund Landau. After completing the work on his thesis, but before writing it up, Kornblum enlisted in the army. He died in the fighting on the Eastern Front. After the war, Landau completed the sad duty of writing up and publishing his student’s results, see Kornblum [1].