Results 101 to 110 of about 130 (120)
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On the maximal unramified pro-2-extension of certain cyclotomic $$\mathbb {Z}_2$$-extensions
Periodica Mathematica Hungarica, 2020Let \({k}\) be a number field and let \({k}_{\infty}\) be the cyclotomic \({\mathbb{Z}}_2\)-extension of \({k}\). Let \(A({k}_n)\) be the \(2\)-Sylow subgroup of the ideal class group of the \(n\)-layer \({k}_n\) of \({k}_{\infty}/{k}\). Let \({\mathcal{L}}({k}_{\infty})\) denote the maximal unramified pro-extension of \({k}_{\infty}\) and \({\mathcal ...
Abdelmalek Azizi +2 more
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On the unramified Kummer extensions of quadratic extensions of the prime cyclotomic number field
Archiv Der Mathematik, 1991exaly +2 more sources
A Leopoldt-Type Result for Rings of Integers of Cyclotomic Extensions
Canadian Mathematical Bulletin, 1995AbstractLet p be a prime number and let m, r denote positive integers with r ≥ 1 if p > 3 (resp. r ≥ 2 if p = 2) and m ≥ 1. We put and Γ = Gd1(N/M). Then the associated order of N/M is the unique maximal order M in the group ring MΓ and ON is a free, rank one module over M. A generator of ON over M is explicitly given.
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A generalization of maillet and demyanenko determinants for the Cyclotomic Zp-Extension
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2001Let \(K\) be an imaginary Abelian field, \(h_K^-\) the relative class number of \(K\). In his previous paper [Acta Arith. 83, 391--397 (1998; Zbl 0895.11045)], the author gave a formula for \(h_K^-\) in the form of a determinant, which generalizes both formulae for Maillet and Demyanenko determinants.
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Kummer Theory over Cyclotomic Zp-extensions
1978In the last chapter we studied the ideal class groups in a Z p -extension of a number field. Here we shall consider especially the cyclotomic Z p -extension, and then Kummer extensions above it, as in Iwasawa [Iw 12], obtained by adjoining p n th roots of units, p-units, and ideal classes of p-power order.
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Heuristics for Anti-cyclotomic ℤ p -extensions
Experimental Mathematics, 2023Debanjana Kundu, Lawrence C. Washington
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Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions
Tohoku Mathematical Journal, 2017Antonio Lei
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Iwasawa invariants of some non-cyclotomic Zp-extensions
Journal of Number Theory, 2018Lawrence Washington
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