Small Zeros of Quadratic Polynomials

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Mathematics (CMC)

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In 1955 J. W. S. Cassels proved that if an integral quadratic form has a non-trivial rational zero then it has such a zero of small height, providing an upper bound on height in terms of the height of the quadratic form. Cassels' result has been extended and generalized in many different ways since. In 1998 D. W. Masser extended Cassels' result to quadratic polynomials by means of considering rational zeros of integral quadratic forms with non-zero first coordinate. I generalize Masser's result by considering small zeros of quadratic forms over a number field outside of a collection of subspaces. If time permits, I will also discuss some related results on algebraic points of small height that satisfy certain arithmetic conditions.

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© 2003 Lenny Fukshansky

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