Results 11 to 20 of about 7,243 (134)

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
doaj   +1 more source

A note on quadratic cyclotomic extensions

, 2022
This paper provides two characterizations of the primitive roots of unity in quadratic cyclotomic extensions over arbitrary fields. Firstly, we introduce a mapping from $\mathbb{N}$ to $\mathbb{N}$ crucial for describing these roots, closely tied to their order over the field.
Marques, Sophie, Mrema, Elizabeth
openaire   +2 more sources

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, Diaz y Diaz, Francisco, Olivier, Michel   +2 more
openaire   +1 more source

Chebyshev Action on Finite Fields [PDF]

, 2013
Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f.
Gassert, T. Alden
core   +1 more source

Artin--Schreier and Cyclotomic Extensions

, 2013
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Salas-Torres, Julio Cesar, Rzedowski-Calderón, Martha, Villa-Salvador, Gabriel   +2 more
openaire   +3 more sources

Extended Genus Fields of Abelian Extensions of Rational Function Fields

Axioms
In this paper, we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. For the general case, we use the fact that the extended genus fields
Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador   +1 more
doaj   +1 more source

The cyclotomic BMW algebra associated with the two string type B braid group

, 2010
The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of type A.
Wilcox, Stewart, Yu, Shona
core   +1 more source

The Chromatic Fourier Transform

Forum of Mathematics, Pi
We 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, Shachar Carmeli, Tomer M. Schlank, Lior Yanovski   +3 more
doaj   +1 more source

On the failure of pseudo-nullity of Iwasawa modules

, 2004
We consider the family of CM-fields which are pro-p p-adic Lie extensions of number fields of dimension at least two, which contain the cyclotomic Z_p-extension, and which are ramified at only finitely many primes.
Romyar, T. Sharifi, Yoshitaka Hachimori
core   +2 more sources

Notes on Number Theory

Mathematics
This 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, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source