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Averages and moments associated to class numbers of imaginary quadratic fields

Abstract:
For any odd prime 𝓁, let $h𝓁(βˆ’d)$ denote the 𝓁-part of the class number of the imaginary quadratic field $Q(βˆšβˆ’d)$. Nontrivial pointwise upper bounds are known only for $𝓁 = 3$; nontrivial upper bounds for averagesof $h𝓁(βˆ’d)$ have previously been known only for $𝓁 = 3, 5$. In this paper we prove nontrivial upper bounds for the average of $h𝓁(βˆ’d)$ for all primes $𝓁 β‰₯ 7$, as well as nontrivial upper bounds for certain higher moments for all primes $𝓁 β‰₯ 3$.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1112/S0010437X1700728X

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Institution:
University of Oxford
Department:
Worcester College
Role:
Author
Publisher:
London Mathematical Society Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
153
Issue:
11
Pages:
2287-2309
Publication date:
2017-08-14
Acceptance date:
2017-02-16
DOI:
Pubs id:
pubs:680541
URN:
uri:a2f49ed5-b78a-40e0-9be5-3ccd24e3619c
UUID:
uuid:a2f49ed5-b78a-40e0-9be5-3ccd24e3619c
Local pid:
pubs:680541
Paper number:
11

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