Results 81 to 90 of about 14,166,488 (203)

Introductory Algebraic Number Theory

, 2003
Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and ...
Saban Alaca, Kenneth S. Williams
core   +1 more source

Elliptic curves with complex multiplication and applications to class field theory [PDF]

, 2022
One of the aims of algebraic number theory is to describe the field of algebraic numbers and the extensions of number fields. This problem appears as the 12° of the 23 Hilbert's problems, and is essentially an extension of the Kronecker-Weber theorem,
Silvestri, Ersilia
core  

Upper bounds for Euclidean minima of algebraic number fields

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor ...
Bayer Fluckiger, Eva
core   +2 more sources

Density of classical points in eigenvarieties [PDF]

, 2011
In this short note, we study the geometry of the eigenvariety parametrizing p-adic automorphic forms for GL(1) over a number field, as constructed by Buzzard. We show that if K is not totally real and contains no CM subfield, points in this space arising
Loeffler, David
core  

Cyclotomic Classes in a Product of Finite Abelian Groups and Applications

Journal of Mathematics
Cyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications.
Somphong Jitman
doaj   +1 more source

Enumeration of rooted 3-connected bipartite planar maps

Comptes Rendus. Mathématique
We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet ...
Noy, Marc, Requilé, Clément, Rué, Juanjo   +2 more
doaj   +1 more source

The theory of algebraic numbers

, 1975
An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases.
Harry Pollard, Harold Diamond, Pollard, Harry, Diamond, Harold G   +3 more
core   +1 more source

x-y duality in topological recursion for exponential variables via quantum dilogarithm

SciPost Physics
For a given spectral curve, the theory of topological recursion generates two different families $\omega_{g,n}$ and $\omega_{g,n}^\vee$ of multi-differentials, which are for algebraic spectral curves related via the universal $x-y$ duality formula.
Alexander Hock
doaj   +1 more source

Fundamental relation on hyper BCI-algebras

Қарағанды университетінің хабаршысы. Математика сериясы
This paper investigates several structural aspects of hyper BCI-algebras and their associated equivalence relations. In particular, we study a notion related to families of hyper BCI-algebras, provide illustrative examples, and analyze the relation β ...
L. Layegh, B. Davvaz
doaj   +1 more source

An Introduction to Algebraic Number Theory

This paper is a whirlwind introduction to the field of algebraic number theory culminating in discussion of Dirichlet’s unit theorem and the class ...
Pattison, Alistair
core   +1 more source