The geometric sieve for quadrics - Browning, Timothy D; Heath-Brown, Roger; New frontiers of the Manin conjecture (Forum Mathematicum, 2021)
We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.
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