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

Autor:	Jaitra Chattopadhyay, S. Muthukrishnan
Rok vydání:	2021
Předmět:	Class (set theory) Algebra and Number Theory Conjecture Mathematics - Number Theory 010102 general mathematics Divisibility rule 01 natural sciences Combinatorics Quadratic equation Integer FOS: Mathematics Number Theory (math.NT) 0101 mathematics Nuclear Experiment Class number Mathematics
Zdroj:	Acta Arithmetica. 197:105-110
ISSN:	1730-6264 0065-1036
DOI:	10.4064/aa200221-16-6
Popis:	Let $k \geq 1$ be 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}. To appear in Acta Arithmetica
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::52dcabdbeaebd070f2a2c833bb7fb56c https://doi.org/10.4064/aa200221-16-6 Zobrazit plný text záznamu