On local laws for the number of small prime factors

Gerald Tenenbaum (1)

1 IECL - Institut Élie Cartan de Lorraine

Investigating a question of Alladi, we describe the local distribution of small prime factors of integers, with emphasis on the transition phase occurring for certain values of the parameters.

Mots clés: local distribution of prime factors; restricted prime factors; small prime factors; saddle-point method.

Domaines: Théorie des nombres [math.NT]

Gerald Tenenbaum. On local laws for the number of small prime factors. Ramanujan Journal, 2020, 51 (1), pp.153-161. ⟨10.1007/s11139-019-00157-w⟩. ⟨hal-02890736⟩