Results 1 to 10 of about 29,642 (86)
Wave Transport and Localization in Prime Number Landscapes
Frontiers 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
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Two-primary algebraic πΎ-theory of rings of integers in number fields [PDF]
Journal 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 βLichtenbaum conjectures.β To
J. Rognes +2 more
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On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field [PDF]
Proceedings 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.
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Algorithmic search for integer Abelian roots of a polynomial with integer Abelian coefficients [PDF]
ΠΠ·Π²Π΅ΡΡΠΈΡ Π‘Π°ΡΠ°ΡΠΎΠ²ΡΠΊΠΎΠ³ΠΎ ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠ°. ΠΠΎΠ²Π°Ρ ΡΠ΅ΡΠΈΡ: ΠΠ°ΡΠ΅ΠΌΠ°ΡΠΈΠΊΠ°. ΠΠ΅Ρ
Π°Π½ΠΈΠΊΠ°. ΠΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΊΠ°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
A Diophantine definition of rational integers over some rings of algebraic numbers. [PDF]
Notre 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 \(K\).
openaire +2 more sources
Nontrivial Galois module structure of cyclotomic fields [PDF]
, 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.
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Algorithms in algebraic number theory [PDF]
, 1992 In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and,
Lenstra Jr., Hendrik W.
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On the integer ring of the compositum of algebraic number fields [PDF]
Nagoya 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.
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Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0 [PDF]
, 2009 Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$, not equal to $K$. We prove the following undecidability results for $R$: If $K$ is recursive, then Hilbert's Tenth Problem is ...
Moret-Bailly, Laurent +1 more
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Similarity and Coincidence Isometries for Modules [PDF]
, 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
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