Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields [PDF]
, 2015 We give criteria of the solvability of the diophantine equation $p=x^2+ny^2$ over some imaginary quadratic fields where $p$ is a prime element. The criteria becomes quite simple in special cases.Comment: 8 pages, This paper has been withdrawn by the ...
Deng, Yingpu, Lv, Chang
core
The Galois theory of the lemniscate [PDF]
, 2012 This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of ...
Cox, David A., Hyde, Trevor
core
p-Capitulation over number fields with p-class rank two
, 2016 Theoretical foundations of a new algorithm for determining the p-capitulation type kappa(K) of a number field K with p-class rank rho=2 are presented. Since kappa(K) alone is insufficient for identifying the second p-class group G=Gal(F(p,2,K) | K) of K,
Mayer, Daniel C.
core +1 more source
No Riemann-hurwitz formula for the p-ranks of relative class groups
, 2015 We disprove, by means of numerical examples, the existence of a Riemann-Hurwitz formula for the p-ranks of relative class groups in a p-ramified p-extension K/k of number fields of CM-type containing ?\_p.
Gras, Georges
core +1 more source
Unit groups of some multiquadratic number fields and 2-class groups. [PDF]
Period Math Hung, 2022 Chems-Eddin MM.
europepmc +1 more source
An explicit Andr\'e-Oort type result for P^1(C) x G_m(C)
, 2014 Using class field theory we prove an explicit result of Andr\'e-Oort type for $\mathbb{P}^1(\mathbb{C}) \times \mathbb{G}_m(\mathbb{C})$. In this variation the special points of $\mathbb{P}^1(\mathbb{C})$ are the singular moduli, while the special points
Paulin, Roland
core
Frobenius and non logarithmic ramification
, 2015 A $\ell$-extension is said logarithmically unramified if it is locally cyclotomic. The purpose of this article is to explain the construction of the logarithmic Frobenius, which plays the role usually played by the classical Frobenius, but in the context
Réglade, Stéphanie
core
Systematic endobronchial ultrasound-guided transbronchial needle aspiration improves radiotherapy planning in non-small cell lung cancer. [PDF]
ERJ Open Res, 2019 Cole AJ +9 more
europepmc +1 more source
Molecular mimicry between Helicobacter pylori antigens and H+, K+ --adenosine triphosphatase in human gastric autoimmunity. [PDF]
J Exp Med, 2003 Amedei A +10 more
europepmc +1 more source
On Hilbert class field tower for some quartic number fields
Arab Journal of Mathematical Sciences, 2021abdelmalek Azizi
exaly