Small zeros of quadratic forms with linear conditions

✍ Scribed by Lenny Fukshansky

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 242 KB
• Volume: 108
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.05.001

✦ Synopsis

Given a quadratic form and M linear forms in N þ 1 variables with coefficients in a number field K; suppose that there exists a point in K Nþ1 at which the quadratic form vanishes and all the linear forms do not. Then we show that there exists a point like this of relatively small height. This generalizes a result of D.W. Masser.