On the growth of the (S,{2})-refined class number
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DOI: 10.1016/j.jnt.2018.12.001
Abstract: We give a new proof of the fact that the growth (with respect to $n$) of the $p$-adic valuation of $h_{n,2}^{-}$ is linear, where $h_{n,2}^{-}$ denotes the minus part of the $(S,\{2\})$-refined class number of… read more here.
Keywords: class number; refined class; growth; number ... See more keywords
A simple criterion for the class number of a quadratic number field to be one
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DOI: 10.1142/s1793042119501033
Abstract: Let [Formula: see text] be a square-free positive integer, [Formula: see text] if [Formula: see text] and [Formula: see text] otherwise. Let [Formula: see text] and [Formula: see text] be integers, where [Formula: see text]… read more here.
Keywords: class number; see text; text formula; formula see ... See more keywords
From the Ideal Theorem to the class number
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DOI: 10.4153/s0008439523000425
Abstract: In this note, we provide an explicit upper bound for $h_K \mathcal{R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem. read more here.
Keywords: theorem class; class number; ideal theorem;