Results 1 to 10 of about 29,705 (142)

A Diophantine definition of rational integers over some rings of algebraic numbers. [PDF]

open access: bronzeNotre Dame Journal of Formal Logic, 1992
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

open access: yesFrontiers in Physics, 2021
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 𝐾-theory of rings of integers in number fields [PDF]

open access: yesJournal of the American Mathematical Society, 1999
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 β€œLichtenbaum conjectures.” To
J. Rognes   +2 more
openaire   +2 more sources

On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field [PDF]

open access: yesProceedings of the American Mathematical Society, 1969
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]

open access: yesΠ˜Π·Π²Π΅ΡΡ‚ΠΈΡ Баратовского унивСрситСта. Новая сСрия: ΠœΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΠΊΠ°. ΠœΠ΅Ρ…Π°Π½ΠΈΠΊΠ°. Π˜Π½Ρ„ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠΊΠ°
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]

open access: yes, 2002
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]

open access: yes, 1997
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]

open access: yesNagoya Mathematical Journal, 1980
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]

open access: yes, 2012
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]

open access: yes, 2010
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

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