A Pair of Quadratic Fields with Class Number Divisible by 3

Himashree Kalita () and Helen K. Saikia ()
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Himashree Kalita: Darrang College, Department of Mathematics
Helen K. Saikia: Gauhati University, Department of Mathematics

A chapter in Class Groups of Number Fields and Related Topics, 2020, pp 141-146 from Springer

Abstract: Abstract Let p be an odd prime and $$\ell \ge 1$$ an integer. In this paper, we prove that the class numbers of $$\mathbb {Q}(\sqrt{p^{12\ell +2}-4})$$ and $$\mathbb {Q}(\sqrt{(4-p^{12\ell }+2)/3})$$ are divisible by 3. Using Siegel’s theorem, we show that there are infinitely many such pairs of quadratic fields with class number divisible by 3.

Keywords: Quadratic field; Class number; Irreducible polynomial; Primary: 11R29; Secondary: 11R11 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-1514-9_13

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DOI: 10.1007/978-981-15-1514-9_13

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