Results 21 to 30 of about 545 (160)
A new formula for the coefficients of Gaussian polynomials
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of ...
Andrica Dorin, Bagdasar Ovidiu
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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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Prime decomposition in the anti-cyclotomic extension [PDF]
Mathematics of Computation, 2007 For an imaginary quadratic number field K K and an odd prime number
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On Nilpotent Extensions of ∞-Categories and the Cyclotomic Trace
International Mathematics Research Notices, 2021 AbstractWe do three things in this paper: (1) study the analog of localization sequences (in the sense of algebraic $K$-theory of stable $\infty $-categories) for additive $\infty $-categories, (2) define the notion of nilpotent extensions for suitable $\infty $-categories and furnish interesting examples such as categorical square-zero extensions, and
Elden Elmanto, Vladimir Sosnilo
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Class group behaviour in cyclotomic extensions of abelian fields [PDF]
, 2021 Let K be a number field. Understanding the ideal class group Cl_K of the field K is a classical problem in algebraic number theory. Solving this problem is hard, especially if the discriminant of the field K is large.
Pagani, Lorenzo
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A Result of Bass on Cyclotomic Extension Fields [PDF]
Proceedings of the American Mathematical Society, 1970 In [1] Bass stated the result given below as Proposition 1 and derived some consequences. His proof of the proposition itself, however, contains a gap; Lemmas 2 and 3 are false as stated. The purpose of this note is to fill the gap by proving the slightly stronger Proposition 2. We retain the notation of [1]. In particular k,,=k(Dm) where A;m = e2rilm.
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Minimal splitting fields in cyclotomic extensions [PDF]
Proceedings of the American Mathematical Society, 1983 Suppose G G is a finite group of exponent
Spiegel, Eugene, Trojan, Allan
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Radical and cyclotomic extensions of the rational numbers [PDF]
Proceedings of the American Mathematical Society, 2007 The principal result in this article is the proof that the Galois closure \(E/\mathbb{Q}\) of a radical extension of the rational numbers \(\mathbb{Q}\) (i.e. an extension \(R = \mathbb{Q}[\alpha]\), where \(\alpha^n \in \mathbb{Q}\) for some positive integer \(n\)) contains a (maximal) cyclotomic extension \(K\) of \(\mathbb{Q}\) whose index in \(E ...
Gluck, David, Isaacs, I. M.
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Iwasawa main conjecture for the Carlitz cyclotomic extension and applications [PDF]
Mathematische Annalen, 2019 Section 3 entirely ...
Bruno Anglès +3 more
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On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions
, 2021 In this paper, we study the length of the $2$-class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$-extensions of the layers $K_n$ of the cyclotomic $\mathbb{Z}_2$-extension of some ...
Azizi, Abdelmalek +2 more
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