Results 1 to 10 of about 29,705 (142)
A Diophantine definition of rational integers over some rings of algebraic numbers. [PDF]
After a negative answer was given to Hilbert's Tenth Problem (that is, is there an algorithm that identifies the diophantine equations which have rational integer solutions and those that don't?) it is natural to ask a similar question in various other domains, for example, in the ring of integers \({\mathcal O}_ K\) of a number field \(K\).
Alexandra Shlapentokh
openalex +3 more sources
Wave Transport and Localization in Prime Number Landscapes
In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields.
Luca Dal Negro +4 more
doaj +1 more source
Two-primary algebraic πΎ-theory of rings of integers in number fields [PDF]
We relate the algebraic K K -theory of the ring of integers in a number field F F to its Γ©tale cohomology. We also relate it to the zeta-function of F F when F F is totally real and Abelian. This establishes the 2 2 -primary part of the βLichtenbaum conjectures.β To
J. Rognes +2 more
openaire +2 more sources
On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field [PDF]
On the basis of these results he conjectured in [9] that the groups Hr(G, OF) have the same order also in the case when G is not cyclic. In the present note, we shall show that the conjecture is false. We shall also demonstrate how the problem of determining Hr(G, OF) can be localized.
Lee, M. P., Madan, M. L.
openaire +1 more source
Algorithmic search for integer Abelian roots of a polynomial with integer Abelian coefficients [PDF]
In this work, we consider the operations over Abelian integers of rank $n$. By definition, such numbers are elements of the complex field and have the form of polynomials with integer coefficients from the $n$th degree primitive root of 1.
Tsybulya, Liliya Mikhailovna
doaj +1 more source
Nontrivial Galois module structure of cyclotomic fields [PDF]
We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-module.
Conrad, Marc, Replogle, Daniel R.
core +5 more sources
On Smarandache's form of the individual Fermat-Euler theorem [PDF]
In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F. SMARANDACHE fits into the generalizations found by S.SCHWARZ, M.LASSAK and the author.
Porubsky, Stefan
core +1 more source
On the integer ring of the compositum of algebraic number fields [PDF]
Let k be an algebraic number field of finite degree. For a finite extension L/k we denote by L/k the different of L/k, and by L the integer ring of L. Let K1 and K2 be finite extensions of k.
openaire +2 more sources
Artin's primitive root conjecture -a survey - [PDF]
This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background.
Moree, Pieter
core +2 more sources
Similarity and Coincidence Isometries for Modules [PDF]
The groups of (linear) similarity and coincidence isometries of certain modules in d-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered.
Adkins +8 more
core +1 more source

