Almost prime solutions to diophantine systems of high rank

Author:

Magyar Ákos1,Titichetrakun Tatchai2

Affiliation:

1. Department of Mathematics, The University of Georgia, Athens, GA 30602, USA

2. Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2, Canada

Abstract

Let [Formula: see text] be a family of [Formula: see text] integral forms of degree [Formula: see text] and [Formula: see text] be a family of pairwise linearly independent linear forms in [Formula: see text] variables [Formula: see text]. We study the number of solutions [Formula: see text] to the diophantine system [Formula: see text] under the restriction that [Formula: see text] has a bounded number of prime factors for each [Formula: see text]. We show that the system [Formula: see text] that has the expected number of such “almost prime” solutions under similar conditions was established for existence of integer solutions by Birch.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

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3. Quadratic forms and systems of forms in many variables;Inventiones mathematicae;2018-02-01

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