Version 1
: Received: 9 October 2024 / Approved: 10 October 2024 / Online: 10 October 2024 (15:23:07 CEST)
How to cite:
WANG, Y.; Zhang, H.; Zhou, Y.; Deng, H.; Li, L. Exploring the 2-Part of Class Groups in Quadratic Fields Perspectives on the Cohen-Lenstra Conjectures. Preprints2024, 2024100808. https://doi.org/10.20944/preprints202410.0808.v1
WANG, Y.; Zhang, H.; Zhou, Y.; Deng, H.; Li, L. Exploring the 2-Part of Class Groups in Quadratic Fields Perspectives on the Cohen-Lenstra Conjectures. Preprints 2024, 2024100808. https://doi.org/10.20944/preprints202410.0808.v1
WANG, Y.; Zhang, H.; Zhou, Y.; Deng, H.; Li, L. Exploring the 2-Part of Class Groups in Quadratic Fields Perspectives on the Cohen-Lenstra Conjectures. Preprints2024, 2024100808. https://doi.org/10.20944/preprints202410.0808.v1
APA Style
WANG, Y., Zhang, H., Zhou, Y., Deng, H., & Li, L. (2024). Exploring the 2-Part of Class Groups in Quadratic Fields Perspectives on the Cohen-Lenstra Conjectures. Preprints. https://doi.org/10.20944/preprints202410.0808.v1
Chicago/Turabian Style
WANG, Y., Haopeng Deng and Lingyue Li. 2024 "Exploring the 2-Part of Class Groups in Quadratic Fields Perspectives on the Cohen-Lenstra Conjectures" Preprints. https://doi.org/10.20944/preprints202410.0808.v1
Abstract
Cohen and Lenstra introduced conjectures concerning the distribution of class numbers in quadratic fields, though many of these conjectures remain unproven. This paper investigates the 2-part of class groups in imaginary quadratic fields and examines their alignment with the Cohen-Lenstra heuristics. We provide detailed proofs of key theorems related to ideal decompositions and modular homomorphisms, and we explore the distribution of class groups of imaginary quadratic fields. Our analysis includes constructing imaginary quadratic fields with prescribed 2-class groups and discussing the implications of these findings on the Cohen-Lenstra conjecture.
Keywords
quadratic fields; class numbers; class groups; Cohen-Lenstra conjecture
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.