Results 1 to 10 of about 4,688 (128)
Determinants on lens spaces and cyclotomic units [PDF]
Journal of Physics A: Mathematical and General, 2004 The Laplacian functional determinants for conformal scalars and coexact one-forms are evaluated in closed form on inhomogeneous lens spaces of certain orders, including all odd primes when the essential part of the expression is given, formally as a ...
Andrews G E +22 more
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Unit Reducible Cyclotomic Fields
, 2023 In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic fields of conductors $2,3,5,7,8,9,12,15$ are all unit reducible, and show that any cyclotomic field of conductor $N$ is not unit reducible if $2^4, 3^3, 5^2, 7^2, 11^2$ or any
Porter, Christian +3 more
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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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Cyclotomic units in function fields [PDF]
Proceedings of the American Mathematical Society, 2008 The relation of cyclotomic units and elliptic units of a number field \(L\) was first studied by \textit{D. Kubert} and \textit{S. Lang} [Bull. Soc. Math. Fr. 107, 161--178 (1979; Zbl 0409.12007)] in the case \(L=\mathbb{Q}(\zeta_p)\) containing \(K=\mathbb{Q}(\sqrt{-p})\), then generalized by \textit{R. Gillard} [Math. Ann.
Bae, Sunghan, Yin, Linsheng
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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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On a duality of Gras between totally positive and primary cyclotomic units [PDF]
, 2016 Let K be a real abelian field of odd degree over Q, and C the group of cyclotomic units of K. We denote by C+ and C0 the totally positive and primary elements of C, respectively. G.
Ichimura, Humio
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Generators and Relations for Cyclotomic Units [PDF]
Nagoya Mathematical Journal, 1966 We prove here an unpublished conjecture of Milnor which gives a complete set of multiplicative relations between the numbers e′(ζ) = 1−ζ,where ranges over complex roots of unity. Information of this type is useful in certain areas of topology as well as in number theory.
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On units generated by Euler systems
, 2009 In the context of cyclotomic fields, it is still unknown whether there exist Euler systems other than the ones derived from cyclotomic units. Nevertheless, we first give an exposition on how norm-compatible units are generated by any Euler system ...
Saikia, Anupam
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A reciprocity map and the two variable p-adic L-function
, 2011 For primes p greater than 3, we propose a conjecture that relates the values of cup products in the Galois cohomology of the maximal unramified outside p extension of a cyclotomic field on cyclotomic p-units to the values of p-adic L-functions of ...
Sharifi, Romyar T.
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Euler complexes and geometry of modular varieties
, 2007 There is a mysterious connection between the multiple polylogarithms at N-th roots of unity and modular varieties. In this paper we "explain" it in the simplest case of the double logarithm. We introduce an Euler complex data on modular curves.
Goncharov, A. B.
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