A note on the simultaneous 3-divisibility of class numbers of tuples of real quadratic fields

Authors

Mohit Mishra, Indian Statistical Institute (Delhi Centre)
Anupam Saikia, Indian Institute of Technology Guwahati

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

Let r be a positive integer, and let k1,k2,⋯,kr be integers such that ki≡±1(mod9) for all 1≤i≤r. In this article, we prove the existence of infinitely many positive integers D such that the class numbers of the real quadratic fields Q(3D),Q(3(D-1)),Q(3(D-k1²)),…,Q(3(D-kr²)) are simultaneously divisible by 3. This result gives an affirmative answer to a weaker version of a conjecture of Iizuka (J Number Theory 184:122–127, 2018).

First Page

465

Last Page

474

DOI

10.1007/s11139-024-00834-5

Publication Date

6-1-2024

Recommended Citation

Mishra, Mohit and Saikia, Anupam, "A note on the simultaneous 3-divisibility of class numbers of tuples of real quadratic fields" (2024). Journal Articles. 4556.
https://digitalcommons.isical.ac.in/journal-articles/4556