STNB2019 (33è any)

A comparative study in an elementary proof of the Prime Number Theorem in Arithmetic Progressions


José Granados


Since that time when Hadamard and De la Vallée-Poussin proved with analytic methods such a impressive result as the Prime Number Theorem, there has been a constant interest in giving not only sharper error terms through advanced and modern methods but also elementary proofs which could offer a more simplistic view of the same result. In addition, arithmetic progressions got into all this stuff and a completely new world appeared: the L-functions, with much importance these days, and the correspondent Prime Number Theorem for Arithmetic Progressions. In this talk, we shall present and compare an elementary proof of this last result by using the ideas Iwaniec and Kowalsky gave to prove the Prime Number Theorem in a primitive form.


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