A quadratic large sieve inequality over number fields

TL;DR

This paper establishes a quadratic large sieve inequality over number fields by introducing and developing the theory of n-th order Hecke families, including a Poisson summation formula variant.

Contribution

It introduces the concept of n-th order Hecke families and proves a large sieve inequality for quadratic characters over number fields.

Findings

Formulated a large sieve inequality for quadratic characters over number fields.

Developed the theory of n-th order Hecke families.

Extended Poisson summation formula to this context.

Abstract

We formulate and prove a large sieve inequality for quadratic characters over a number field. To do this, we introduce the notion of an n-th order Hecke family. We develop the basic theory of these Hecke families, including versions of the Poisson summation formula.