Results 31 to 40 of about 545 (160)
Artin--Schreier and Cyclotomic Extensions
, 2013 10 ...
Salas-Torres, Julio Cesar +2 more
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Cyclotomic extensions of number fields
Indagationes Mathematicae, 2003 Let \(K\) be a number field, \(l\) a prime number, and \(\zeta_l\) a primitive \(l\)th root of unity. The paper is devoted to the cyclotomic extension \(K(\zeta_l)/K\), giving explicit formulae for the discriminant, conductor, and different of this extension.
Cohen, Henri +2 more
openaire +1 more source
The Chromatic Fourier Transform
Forum of Mathematics, PiWe develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$ , as well as a certain duality for the $E_n$ -(co)homology of $\pi
Tobias Barthel +3 more
doaj +1 more source
Some Questions on the Ideal Class Group of Imaginary Abelian Fields
, 2007 Let k be an imaginary quadratic field. Assume that the class number of k is exactly an odd prime number p, and p splits into two distinct primes in k. Then it is known that a prime ideal lying above p is not principal.
Itoh, Tsuyoshi
core +1 more source
MathematicsThis paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-
Miroslav Stoenchev +2 more
doaj +1 more source
Wilson's map operations on regulat dessins and cyclotomic fields of definition
, 2009 Dessins d’enfants can be seen as bipartite graphs embedded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, even an algebraic structure as a projective algebraic curve ...
Streit, M. +3 more
core +1 more source
Cyclotomic extensions and the Kronecker-Weber theorem
, 2023 In the thesis, we prove the Kronecker-Weber theorem, which states that every abelian extension of the field of rational numbers is a subfield of some cyclotomic field.
Jarrahová, Veronika
core +1 more source
Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381
Transactions on Cryptographic Hardware and Embedded SystemsNon-degenerate bilinear maps on elliptic curves, commonly referred to as pairings, have many applications including short signature schemes, zero-knowledge proofs and remote attestation protocols.
Hao Cheng +3 more
doaj +1 more source
The 3‐sparsity of Xn−1$X^n-1$ over finite fields of characteristic 2
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract Let q$q$ be a prime power and Fq$\mathbb {F}_q$ the finite field with q$q$ elements. For a positive integer n$n$, the polynomial Xn−1∈Fq[X]$X^n - 1 \in \mathbb {F}_q[X]$ is termed 3‐sparse over Fq$\mathbb {F}_q$ if all its irreducible factors in Fq[X]$\mathbb {F}_q[X]$ are either binomials or trinomials.
Kaimin Cheng
wiley +1 more source
Infinite families of cyclotomic function fields with any prescribed class group rank
, 2021 We prove the existence of the maximal real subfields of cyclotomic extensions over the rational function field k = F-q(T) whose class groups can have arbitrarily large l(n)-rank, where F-q is the finite field of prime power order q.
Lee, Yoonjin, Yoo, Jinjoo
core +2 more sources