Results 31 to 40 of about 217 (158)
Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm
Complexity, 2020 Sequences with high linear complexity property are of importance in applications. In this paper, based on the theory of generalized cyclotomy, new classes of quaternary generalized cyclotomic sequences with order 4 and period 2pm are constructed.
Pinhui Ke, Yan Zhong, Shengyuan Zhang
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Almost Difference Sets from Unions of Cyclotomic Classes of Order 10
Recoletos Multidisciplinary Research JournalThis study investigated the problem of constructing almost difference sets from single and unions of cyclotomic classes of order 10 (with and without zero) of the finite field GF(q), where q is a prime of the form q = 10n+1 for integer n≥1 and ...
Benedict Estrella
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THE HEIGHT OF A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS
Bulletin of the Korean Mathematical Society, 2017 exaly +3 more sources
Class number parity for the $p$th cyclotomic field [PDF]
Mathematics of Computation, 1994 Let \(p\) be an odd prime and let \(h_ p= h^ -_ p h^ +_ p\) denote the class number of the \(p\)-th cyclotomic field. It was \textit{E. E. Kummer} (1870) [Collected papers, p. 925, (III.) (1975; Zbl 0327.01019)] who proved the statement: ``\(2\mid h^ +_ p \Rightarrow 2\mid h^ - _ p\)''. This paper deals with the parity of \(h_ p\) in the case that \(p\)
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Localization sequences for logarithmic topological cyclic homology
Journal of Topology, Volume 19, Issue 3, September 2026.Abstract We introduce the notion of an Ek$\mathbb {E}_k$‐ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories. Our approach is based on Thom R$R$‐algebras.
John Rognes +2 more
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Factorization of Graded Traces on Nichols Algebras
Axioms, 2017 A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of ...
Simon Lentner, Andreas Lochmann
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A generalisation of Cameron's base size conjecture
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract Let G⩽Sym(Ω)$G\leqslant {\rm Sym}(\Omega)$ be a finite transitive permutation group with point stabiliser H$H$. A base for G$G$ is a subset of Ω$\Omega$ whose pointwise stabiliser is trivial, and the minimal cardinality of a base is called the base size of G$G$, denoted by b(G,Ω)$b(G, \Omega)$. Equivalently, b(G,Ω)$b(G, \Omega)$ is the minimal
Marina Anagnostopoulou‐Merkouri
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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 $p ...
Georges Gras
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A trace–path integral formula over function fields
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We show that an arithmetic path integral over the ℓ$\ell$‐torsion of a Jacobian J[ℓ]$J[\ell]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ])$H(J[\ell])$, up to an explicitly determined sign.
Yan Yau Cheng
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On the class numbers of cyclotomic fields
Journal of Number Theory, 1973 AbstractLet gn denote the first factor of the class number of the nth cyclotomic field. It is proved that if n runs through a sequence of prime powers pr tending to infinity, then log gn ∼ 14 [1 − (1p)]n log n.
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