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Weber's class number problem and its variants

Published 28 Nov 2022 in math.NT and math.GT | (2211.15201v1)

Abstract: We survey Weber's class number problem and its variants in the spirit of arithmetic topology; we recollect some history, present a relation to certain units and generalized Pell's equation, and overview a study of the $p$-adic limits of class numbers in $\mathbb{Z}_p$-towers together with numerical investigation for knots and elliptic curves.

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