A collage of results on the divisibility and indivisibility of class numbers of quadratic fields

Srilakshmi KrishnamoorthySunil Kumar PasupulatiMuneeswaran R

Nov 2023

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The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of research on many topics linked to quadratic field class groups notably intriguing aspect is the divisibility of the class numbers. This article discusses a few recent results on the divisibility of class numbers and the Izuka conjecture. We also discuss the quantitative aspect of the Izuka conjecture.

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