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The approximate Determinant Method and some applications

Wed 30 January 2013, 10:00

Thomas Reuss
Oxford

Linfoot

Organiser: Tim Browning

ABSTRACT
We show how the Heath-Brown Determinant Method can be used to obtain an
upper bound for the number of integral points (d,e,u,v) on the variety
defined by
e^2v-d^2u=1. We will illustrate how the ideas involved lead to asymptotic
formulas for the number of r-tuples of k-free integers up to X, and
the number of consecutive square-full integers up to X. We will illustrate
a further application to the size of the fundamental solution of Pell
Equations.