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ON QUADRATIC FIELDS GENERATED BY POLYNOMIALS
Part of:
Multiplicative number theory
Algebraic number theory: global fields
Exponential sums and character sums
Published online by Cambridge University Press: 29 June 2023
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.
MSC classification
Primary:
11L40: Estimates on character sums
Information
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
During the preparation of this work, the author was supported by the Australian Research Council Grant DP200100355.
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