Consecutive real quadratic fields with large class numbers

Abstract

For a given positive integer $k$, we prove that there are at least $x^{1/2-o(1)}$ integers $d\le x$ such that the real quadratic fields $\mathbb{Q}(\sqrt{d+1}),\dots ,\mathbb{Q}(\sqrt{d+k})$ have class numbers essentially as large as possible.

7 pages; strengthened the results and added a co-author; comments are welcome!

Cited by in corpus (3)

• Universal quadratic forms and indecomposables in number fields: A survey
• On continued fraction partial quotients of square roots of primes
• On abelian cubic fields with large class number