Signature ranks of units in cyclotomic extensions of abelian number fields [PDF]
Pacific Journal of Mathematics, 2018 We prove the rank of the group of signatures of the circular units (hence also the full group of units) of ${\mathbb Q}( \zeta_m)^+$ tends to infinity with $m$.
D. Dummit, Evan P. Dummit, H. Kisilevsky
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A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE RANKS OF UNITS IN CYCLOTOMIC FIELDS [PDF]
Nagoya mathematical journal, 2018 We collect some statements regarding equivalence of the parities of various class numbers and signature ranks of units in prime power cyclotomic fields. We correct some misstatements in the literature regarding these parities by providing an example of a
D. Dummit
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Annihilation of $\text{tor}_{Z_{p}}(\mathcal G_{K,S}^{ab})$ for real abelian extensions $K/Q$
Communications in Advanced Mathematical Sciences, 2018 Let $K$ be a real abelian extension of $\mathbb{Q}$. Let $p$ be a prime number, $S$ the set of $p$-places of $K$ and ${\mathcal G}_{K,S}$ the Galois group of the maximal $S \cup \{\infty\}$-ramified pro-$p$-extension of $K$ (i.e., unramified outside $p ...
Georges Gras
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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
Forum of Mathematics, Pi, 2015 Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
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Cyclotomic units and class groups in p-extensions of real abelian fields [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2008 For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic p-extension of F.
Filippo A. E. Nuccio
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Cohomology groups of cyclotomic units
, 1992 Let d be a positive integer and p be and odd prime such that (p, d) = 1 and p 1 p(d), where cp is the Euler q function. For each n 2 1 let K,,=Q([g+~,) and K,x =U,, K,,, where [,=e 2rri’n* is a primitive m th root of 1 for any m > 0. Then K, is the basic
J. Kim
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Note on Cyclotomic Units and Gauss Sums in Local Cyclotomic Fields
, 2001 the Hilbert norm residue symbol at p. There are canonical subgroups Cn and Gn of Un generated by certain cyclotomic units and certain Gauss sums, respectively. (For the definition of Gn , see [8, Section 5.1].) We first show that these subgroups are ``in
H. Ichimura
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Entanglement-Assisted Quantum Codes from Cyclic Codes. [PDF]
Entropy (Basel), 2022 Pereira FRF, Mancini S.
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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes. [PDF]
Entropy (Basel), 2023 Chen J +7 more
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]
Period Math Hung, 2022 Chems-Eddin MM.
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