Linear equations and heights over division algebras

✍ Scribed by Christine Liebendörfer

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 389 KB
• Volume: 105
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.09.003

✦ Synopsis

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.