Lagrange's Four Squares Theorem with almost prime variables.

Abstract

In 1994, Brüdern and Fouvry [1] initiated the investigation of Lagrange's four squares theorem with almost prime variables.In this paper, we prove that every sufficiently large integer, congruent to 4 modulo 24, can be represented as a sum of four squares of integers, each of which has at most four prime factors.Instead of the four-dimensional vector sieve developed by Brüdern and Fouvry [1], we establish this result by combining the threedimensional sieve and the switching principle.

Locations

• The HKU Scholars Hub (University of Hong Kong) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View