Totally positive algebraic integers of small trace

Chistopher J. Smyth

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 3, page 1-28
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Smyth, Chistopher J.. "Totally positive algebraic integers of small trace." Annales de l'institut Fourier 34.3 (1984): 1-28. <http://eudml.org/doc/74643>.

@article{Smyth1984,
abstract = {Let $\alpha $ 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 $\alpha $, and display the resulting list of 1314 values of $\alpha $ which the algorithm produces.},
author = {Smyth, Chistopher J.},
journal = {Annales de l'institut Fourier},
keywords = {difference between trace and degree at most 6; list of values; totally positive algebraic integer; algorithm},
language = {eng},
number = {3},
pages = {1-28},
publisher = {Association des Annales de l'Institut Fourier},
title = {Totally positive algebraic integers of small trace},
url = {http://eudml.org/doc/74643},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Smyth, Chistopher J.
TI - Totally positive algebraic integers of small trace
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 3
SP - 1
EP - 28
AB - Let $\alpha $ 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 $\alpha $, and display the resulting list of 1314 values of $\alpha $ which the algorithm produces.
LA - eng
KW - difference between trace and degree at most 6; list of values; totally positive algebraic integer; algorithm
UR - http://eudml.org/doc/74643
ER -

References

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  1. [1] E.W. CHENEY, Introduction to approximation theory, McGraw-Hill, New York, 1966. Zbl0161.25202MR36 #5568
  2. [2] R.M. ROBINSON, Algebraic equations with span less than 4, Math. of Comp., 10 (1964), 549-559. Zbl0147.12905
  3. [3] C.L. SIEGEL, The trace of totally positive and real algebraic integers, Ann Math., 46 (1945), 302-312. Zbl0063.07009MR6,257a
  4. [4] C.J. SMYTH, On the measure of totally real algebraic integers II, Math. of Comp., 37 (1981), 205-208. Zbl0475.12001MR82j:12002b
  5. [5] C.J. SMYTH, The mean values of totally real algebraic integers, Math. of Comp., to appear April 1984. Zbl0536.12006MR86e:11115

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