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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Milner 216

Thursdays, 1:00-2:00 PM

**Lenny Fukshansky**

University of Texas

**Thursday, November 6**

Milner 216, 1:00 PM

**Title:** *Small zeros of quadratic polynomials*

**Abstract:** 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.