Journal article

### Averages and moments associated to class numbers of imaginary quadratic fields

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

### Access Document

Files:
• (pdf, 381.0KB)
Publisher copy:
10.1112/S0010437X1700728X

### Authors

More by this author
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