Totally positive algebraic integers of small trace
Annales de l'Institut Fourier, Tome 34 (1984) no. 3, pp. 1-28.

Soit α un entier algébrique totalement positif, dont la différence entre la trace et le degré n’excède pas 6. On décrit un algorithme pour trouver tous les α de ce type, et on donne la table des 1314 valeurs de α issues de l’algorithme.

Let α be a totally positive algebraic integer, with the difference between its trace and its degree at most 6. We describe an algorithm for finding all such α, and display the resulting list of 1314 values of α which the algorithm produces.

@article{AIF_1984__34_3_1_0,
     author = {Smyth, Chistopher J.},
     title = {Totally positive algebraic integers of small trace},
     journal = {Annales de l'Institut Fourier},
     pages = {1--28},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {34},
     number = {3},
     year = {1984},
     doi = {10.5802/aif.975},
     zbl = {0534.12002},
     mrnumber = {86f:11091},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.975/}
}
TY  - JOUR
AU  - Smyth, Chistopher J.
TI  - Totally positive algebraic integers of small trace
JO  - Annales de l'Institut Fourier
PY  - 1984
DA  - 1984///
SP  - 1
EP  - 28
VL  - 34
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.975/
UR  - https://zbmath.org/?q=an%3A0534.12002
UR  - https://www.ams.org/mathscinet-getitem?mr=86f:11091
UR  - https://doi.org/10.5802/aif.975
DO  - 10.5802/aif.975
LA  - en
ID  - AIF_1984__34_3_1_0
ER  - 
Smyth, Chistopher J. Totally positive algebraic integers of small trace. Annales de l'Institut Fourier, Tome 34 (1984) no. 3, pp. 1-28. doi : 10.5802/aif.975. http://archive.numdam.org/articles/10.5802/aif.975/

[1] E.W. Cheney, Introduction to approximation theory, McGraw-Hill, New York, 1966. | MR 36 #5568 | Zbl 0161.25202

[2] R.M. Robinson, Algebraic equations with span less than 4, Math. of Comp., 10 (1964), 549-559. | Zbl 0147.12905

[3] C.L. Siegel, The trace of totally positive and real algebraic integers, Ann Math., 46 (1945), 302-312. | MR 6,257a | Zbl 0063.07009

[4] C.J. Smyth, On the measure of totally real algebraic integers II, Math. of Comp., 37 (1981), 205-208. | MR 82j:12002b | Zbl 0475.12001

[5] C.J. Smyth, The mean values of totally real algebraic integers, Math. of Comp., to appear April 1984. | MR 86e:11115 | Zbl 0536.12006

Cité par Sources :