Divisibility of the class numbers of imaginary quadratic fields

By K. Chakraborty, Azizul Hoque, Y. Kishi, P. P. Pandey. 2017

50 citations recorded by the source corpus.

For a given odd integer $n>1$, we provide some families of imaginary quadratic number fields of the form $\mathbb{Q}(\sqrt{x^2-t^n})$ whose ideal class group has a subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c3e9c48b120c1e692c03c2aaa6fdb5852bf51856

How researchers see this paper

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In Algebra and Number Theory

1. Melanie Matchett Wood
2. Jordan S. Ellenberg
3. L. Pierce
4. Akshay Venkatesh
5. Kiran S. Kedlaya
6. Dan Erik Petersen

In Applied Mathematics

1. L. Pierce
2. Melanie Matchett Wood

In Geometry and Topology

1. Melanie Matchett Wood
2. L. Pierce
3. Jordan S. Ellenberg
4. Dan Erik Petersen
5. Akshay Venkatesh
6. Kiran S. Kedlaya
7. Michael A. Bennett

Citations in the corpus

• On ℓ-torsion in class groups of number fields (2016, background): “In this vein, in the case of imaginary quadratic fields, Soundararajan [Sou00] noted that for all but at most one imaginary quadratic field K with DK ∈ [X, 2X ], one has the bound |ClK [l]| ≪ X1/2−1/2l+ε, for any prime l.”