Linear equations and heights over division algebras

JOURNAL OF NUMBER THEORY

卷:105

Article

Liebendörfer, C

关键词: heights;    division algebras;    quaternion algebras;    linear equations;   

DOI  :  10.1016/j.jnt.2003.09.003

来源: Elsevier

【 摘 要 】

We make a start on the investigation of small solutions to systems of homogeneous linear equations over non-commutative division algebras. In this paper we prove some upper and lower bounds for the sizes of solutions to such systems. To measure solutions and coefficient matrices we define heights which satisfy natural invariance and finiteness properties. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free