- Abstract:
- For any odd prime π, let $hπ(βd)$ denote the π-part of the class number of the imaginary quadratic field $Q(ββd)$. Nontrivial pointwise upper bounds are known only for $π = 3$; nontrivial upper bounds for averagesof $hπ(βd)$ have previously been known only for $π = 3, 5$. In this paper we prove nontrivial upper bounds for the average of $hπ(βd)$ for all primes $π β₯ 7$, as well as nontrivial upper bounds for certain higher moments for all primes $π β₯ 3$.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted manuscript
- Files:
-
-
(pdf, 381.0KB)
-
- Publisher copy:
- 10.1112/S0010437X1700728X
-
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- Funding agency for:
- Heath-Brown, D
- 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
- Copyright holder:
- Heath-Brown and Pierce
- Copyright date:
- 2017
- Notes:
- Β© the Author(s) 2017. This journal is Β© Foundation Compositio Mathematica 2017. This is the accepted manuscript version of the article. The final version is available online from CUP at: 10.1112/S0010437X1700728X
Journal article
Averages and moments associated to class numbers of imaginary quadratic fields
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