The R₂ measure for totally positive algebraic integers

V. Flammang. "The R₂ measure for totally positive algebraic integers." Colloquium Mathematicae 144.1 (2016): 45-53. <http://eudml.org/doc/283710>.

@article{V2016,
abstract = {Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates $α₁ = α,..., α_\{d\}$ are positive real numbers. We study the set ₂ of the quantities $(∏_\{i=1\}^\{d\} (1 + α²_\{i\})^\{1/2\})^\{1/d\}$. We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.},
author = {V. Flammang},
journal = {Colloquium Mathematicae},
keywords = {algebraic integers; measure; auxiliary functions},
language = {eng},
number = {1},
pages = {45-53},
title = {The R₂ measure for totally positive algebraic integers},
url = {http://eudml.org/doc/283710},
volume = {144},
year = {2016},
}

TY - JOUR
AU - V. Flammang
TI - The R₂ measure for totally positive algebraic integers
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 1
SP - 45
EP - 53
AB - Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates $α₁ = α,..., α_{d}$ are positive real numbers. We study the set ₂ of the quantities $(∏_{i=1}^{d} (1 + α²_{i})^{1/2})^{1/d}$. We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.
LA - eng
KW - algebraic integers; measure; auxiliary functions
UR - http://eudml.org/doc/283710
ER -