Counting ideals in ray classes

Olivier Ramaré (1) , Sanoli Gun (2) , Jyothsnaa Sivaraman

1 I2M - Institut de Mathématiques de Marseille
2 IMSc - Institute of Mathematical Sciences [Chennai]

Let K be a number field and q an integral ideal in O K. A result of Tatuzawa [11] from 1973, computes the asymptotic (with an error term) for the number of ideals with norm at most x in a class of the narrow ray class group of K modulo q. This result bounds the error term with a constant whose dependence on q is explicit but dependence on K is not explicit. The aim of this paper is to prove this asymptotic with a fully explicit bound for the error term.

Domaines: Théorie des nombres [math.NT]

Olivier Ramaré, Sanoli Gun, Jyothsnaa Sivaraman. Counting ideals in ray classes. Journal of Number Theory, 2022, 243, pp.13 - 37. ⟨10.1016/j.jnt.2022.08.005⟩. ⟨hal-03805062⟩