Results 41 to 50 of about 1,812,540 (189)
Wilson's map operations on regulat dessins and cyclotomic fields of definition
, 2009 Dessins d’enfants can be seen as bipartite graphs embedded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, even an algebraic structure as a projective algebraic curve ...
Streit, M. +3 more
core +1 more source
Complementary dual abelian codes in group algebras of some finite abelian groups [PDF]
ITM Web of ConferencesLinear complementary dual codes have become an interesting sub-family of linear codes over finite fields since they can be practically applied in various fields such as cryptography and quantum error-correction. Recently, properties of complementary dual
Jitman Somphong
doaj +1 more source
Cyclotomic polynomials and units in cyclotomic number fields
Journal of Number Theory, 1988 The author proves (theorem 1) that if P(x)\(\neq x\) is a monic irreducible polynomial with integer coefficients such that its resultant with infinitely many cyclotomic polynomials is \(+1\) or -1, then P(x) is a cyclotomic polynomial. From this he deduces a number of interesting corollaries: for example, if \(\alpha\neq 0\) is an algebraic integer ...
openaire +1 more source
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
wiley +1 more source
On some exact sequences in the theory of cyclotomic fields [PDF]
, 2008 The purpose of this article is to show the existence of some exact sequences which relate the ideal class groups of cyclotomic fields to Gauss sums. These exact sequences imply the results of Hachimori, Ichimura and Beliaeva.
Aoki, Miho
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Factor-4 and 6 compression of cyclotomic subgroups of and
Journal of Mathematical Cryptology, 2010 Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields 𝔽2m and 𝔽3m, respectively, have been used to implement pairing-based cryptographic protocols.
Karabina Koray
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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
wiley +1 more source
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
wiley +1 more source
Bounds for class numbers of cyclotomic function fields.
, 2000 Class groups---and their size, the class number---give information about the arithmetic within a field. For example, if a field has class number one, then integers within the field will factor uniquely (as they do in Z ).
Palen, Joseph John
core +5 more sources
Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
IEEE Access, 2019 The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
doaj +1 more source