Arithmetic progressions in binary quadratic forms and norm forms

被引：1

作者：

Elsholtz, Christian ^{[1
]}

Frei, Christopher ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Anal & Zahlentheorie, Kopernikusgasse 24-2, A-8010 Graz, Austria

[2] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2019年 / 51卷 / 04期

关键词：

11E25; 11D57 (primary); 11E12 (secondary);

D O I：

10.1112/blms.12256

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove an upper bound for the length of an arithmetic progression represented by an irreducible integral binary quadratic form or a norm form, which depends only on the form and the progression's common difference. For quadratic forms, this improves significantly upon an earlier result of Dey and Thangadurai.

引用

页码：595 / 602

页数：8

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