On a Shintani decomposition for a cubic field defined by X3 + kX - 1 = 0

Number Theory ◽  
2012 ◽  
Author(s):  
Ryotaro Okazaki
Keyword(s):  
Cubic Field

The determination of units in totally real cubic fields

1960 ◽  
Vol 56 (4) ◽  
pp. 318-321 ◽  
Author(s):  
H. J. Godwin
Keyword(s):  
Trial And Error ◽  
Integral Lattice ◽  
Cubic Field ◽  
Cubic Fields ◽  
Trial And Error Method ◽  
Totally Real ◽  
Rational Integral ◽  
Fundamental Units ◽  
Error Method

The determination of a pair of fundamental units in a totally real cubic field involves two operations—finding a pair of independent units (i.e. such that neither is a power of the other) and from these a pair of fundamental units (i.e. a pair ε1; ε2 such that every unit of the field is of the form with rational integral m, n). The first operation may be accomplished by exploring regions of the integral lattice in which two conjugates are small or else by factorizing small primes and comparing different factorizations—a trial-and-error method, but often a quick one. The second operation is accomplished by obtaining inequalities which must be satisfied by a fundamental unit and its conjugates and finding whether or not a unit exists satisfying these inequalities. Recently Billevitch ((1), (2)) has given a method, of the nature of an extension of the first method mentioned above, which involves less work on the second operation but no less on the first.

On the occurrence of a metastable tetragonal t′-phase in a ZrO2−13.6 mole % MgO ceramic and its microscopic thermal evolution

1993 ◽  
Vol 8 (3) ◽  
pp. 605-610 ◽  
Author(s):  
M.C. Caracoche ◽  
P.C. Rivas ◽  
A.F. Pasquevich ◽  
A.R. López García ◽  
E. Aglietti ◽  
...  
Keyword(s):  
Thermal Behavior ◽  
Room Temperature ◽  
Oxygen Vacancies ◽  
Single Phase ◽  
Thermal Evolution ◽  
Hyperfine Interactions ◽  
Correlation Technique ◽  
Cubic Field ◽  
Time Differential ◽  
T Phase

The time-differential perturbed angular correlation technique has been used to investigate the thermal behavior of a ZrO2−13.6 mole % MgO ceramic between room temperature and 1423 K. Two different quadrupole hyperfine interactions corresponding to a tetragonal structure have been found to result on cooling the ceramic from the single-phase cubic field. One of them agrees with that depicting the pure t-ZrO2 tetragonal phase and the other one has been interpreted as describing a high-MgO-content nontransformable t'–ZrO2 phase. As temperature increases, the latter gives rise to a similar but fluctuating interaction related to the oxygen vacancies mobility and which shows a thermal behavior analogous to that already reported for the stabilized cubic ZrO2. Above 1100 K these dynamic t'-sites transform into pure tetragonal ones which behave ordinarily, suffering the t → m phase transition when cooling to room temperature. Differences found between TDPAC results and information drawn from other techniques are discussed.

scholarly journals Remarks on principal factors in a relative cubic field

1971 ◽  
Vol 3 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Pierre Barrucand ◽  
Harvey Cohn
Keyword(s):  
Cubic Field ◽  
Principal Factors

Ground-State Splitting ford5S6Ions in a Cubic Field

1960 ◽  
Vol 5 (4) ◽  
pp. 145-146 ◽  
Author(s):  
M. J. D. Powell ◽  
J. R. Gabriel ◽  
D. F. Johnston
Keyword(s):  
Ground State ◽  
Cubic Field ◽  
State Splitting

Zeeman Effect of the Purely Cubic Field Fluorescence Line of MgO:Cr3+Crystals

1960 ◽  
Vol 120 (6) ◽  
pp. 2045-2053 ◽  
Author(s):  
S. Sugano ◽  
A. L. Schawlow ◽  
F. Varsanyi
Keyword(s):  
Zeeman Effect ◽  
Cubic Field ◽  
Fluorescence Line

Observation of the cubic‐field splitting of an excited S=2 manifold in a cubic copper tetramer

1984 ◽  
Vol 80 (10) ◽  
pp. 4620-4624 ◽  
Author(s):  
T. D. Black ◽  
R. S. Rubins ◽  
D. K. De ◽  
Richard C. Dickinson ◽  
W. A. Baker
Keyword(s):  
Field Splitting ◽  
Cubic Field

scholarly journals On unramified cyclic extensions of degree l of algebraic number fields of degree l

1987 ◽  
Vol 107 ◽  
pp. 135-146 ◽  
Author(s):  
Yoshitaka Odai
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Preceding Paper ◽  
Algebraic Number Field ◽  
Number Fields ◽  
Maximal Extension ◽  
Algebraic Number Fields ◽  
Cubic Field ◽  
Genus Field ◽  
Abelian Number Field

Let I be an odd prime number and let K be an algebraic number field of degree I. Let M denote the genus field of K, i.e., the maximal extension of K which is a composite of an absolute abelian number field with K and is unramified at all the finite primes of K. In [4] Ishida has explicitly constructed M. Therefore it is of some interest to investigate unramified cyclic extensions of K of degree l, which are not contained in M. In the preceding paper [6] we have obtained some results about this problem in the case that K is a pure cubic field. The purpose of this paper is to extend those results.

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