On the simultaneous 3-divisibility of class numbers of triples of imaginary quadratic fields

Published on Jan 1, 2021in Acta Arithmetica0.608
· DOI :10.4064/AA200221-16-6
Jaitra Chattopadhyay3
Estimated H-index: 3
,
S. Muthukrishnan27
Estimated H-index: 27
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Abstract
Let k \geq 1be a cube-free integer with k \equiv 1 \pmod {9}and \gcd(k, 7\cdot 571)=1 In this paper, we prove the existence of infinitely many triples of imaginary quadratic fields \mathbb{Q}(\sqrt{d}) \mathbb{Q}(\sqrt{d+1})and \mathbb{Q}(\sqrt{d+k^2})with d \in \mathbb{Z}such that the class number of each of them is divisible by 3 This affirmatively answers a weaker version of a conjecture of Iizuka \cite{iizuka-jnt}.
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2011
1 Author (Katsumasa Ishii)
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Abstract null null Text null For a given odd positive integer n and an odd prime p, we construct an infinite family of quadruples of imaginary quadratic fields null null null Q null ( null null null d null null null ) null null , null null null Q null ( null null null d null + null 1 null null null ) null null , null null null Q null ( null null null d null + null 4 null null null ) null null null and null null null Q null ( null null null d null + null 4 null null null p null null null 2 null n...
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#1Jaitra Chattopadhyay (IITG: Indian Institute of Technology Guwahati)H-Index: 3
#2Anupam Saikia (IITG: Indian Institute of Technology Guwahati)H-Index: 5
For a square-free integer t, Byeon (Proc. Am. Math. Soc. 132:3137–3140, 2004) proved the existence of infinitely many pairs of quadratic fields null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null $\mathbb {Q}(\sqrt{D}) null null null null null null null null ...
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