Abstract
Abstract
Let
$f(X) \in {\mathbb Z}[X]$
be a polynomial of degree
$d \ge 2$
without multiple roots and let
${\mathcal F}(N)$
be the set of Farey fractions of order N. We use bounds for some new character sums and the square-sieve to obtain upper bounds, pointwise and on average, on the number of fields
${\mathbb Q}(\sqrt {f(r)})$
for
$r\in {\mathcal F}(N)$
, with a given discriminant.
Publisher
Cambridge University Press (CUP)
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