Universal quadratic forms over polynomial rings

Myung-Hwan Kim; Yuanhua Wang; Fei Xu

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2008; 45(5): 1311-1322

Printed September 1, 2008

Universal quadratic forms over polynomial rings

Myung-Hwan Kim, Yuanhua Wang, and Fei Xu

Seoul National University, Chinese Academy of Sciences, Chinese Academy of Sciences

Abstract

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Abstract

The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the $Four$ $Conjecture$ proposed by Gerstein.

Keywords: universal forms over polynomial rings, the Four conjecture

MSC numbers: Primary 11E12, 11E08