Bases of Analytic Number Theory

Joel Rivat (1)

1 I2M - Institut de Mathématiques de Marseille

These lecture notes were written in French in 2000 with no plan to be published, and I used them several times to give lectures. Many thanks to Sébastien Ferenczi for the English translation. They should not be compared with reference books like Tenenbaum [6], Iwaniec and Kowalski [3] and Montgomery and Vaughan [4], but an invitation to read these books. The zeta function part owes much to Davenport’s book [1]. The chapter on the large sieve uses the complete works of Selberg [5]. Our upper bounds on exponential sums are adapted from Graham and Kolesnik [2], with an effort to make the constants explicit but without attempting at optimality; they were then used later by Tenenbaum [6]. We think that the constant factor 16 instead of 2π2 in the Bombieri-Iwaniec inequality (Theorem 6.38) is new.

Domaines: Théorie des nombres [math.NT]

Joel Rivat. Bases of Analytic Number Theory. Ferenczi, S; KulagaPrzymus, J; Lemanczyk, M. ERGODIC THEORY AND DYNAMICAL SYSTEMS IN THEIR INTERACTIONS WITH ARITHMETICS AND COMBINATORICS, 2213, SPRINGER INTERNATIONAL PUBLISHING AG, pp.1-2, 2018, Lecture Notes in Mathematics, 978-3-319-74908-2; 978-3-319-74907-5. ⟨hal-02017147⟩