Pretentious multiplicative functions and the prime number theorem for arithmetic progressions (Q2841768)

We quote the author's perfect summary: ``Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.''NEWLINENEWLINEHere the author gives an optimal example of \textit{A. Granville} and \textit{K. Soundararajan}'s elementary approach in [``Multiplicative number theory: the pretentious approach'' (to appear)], involving a property of multiplicative functions, the so-called ``pretentious''.NEWLINENEWLINEThe reviewer thinks that, apart from the importance of the main result (Theorem 1.1, building on Siegel's Theorem, here proved in a simpler fashion, namely see Theorem 1.2 proof) and from the wealth of results disseminated along the path of its (mainly, elementary) proof, the present paper is a kind of map for analytic number theorists who want to enter the realm of ``pretentious'', so to speak, methods.