The Trace of Totally Positive and Real Algebraic Integers

1945 ◽  
Vol 46 (2) ◽  
pp. 302 ◽  
Author(s):  
Carl Ludwig Siegel
Keyword(s):  
Algebraic Integers ◽  
Totally Positive

scholarly journals Computing totally positive algebraic integers of small trace

2011 ◽  
Vol 80 (274) ◽  
pp. 1041-1041 ◽  
Author(s):  
James McKee
Keyword(s):  
Algebraic Integers ◽  
Totally Positive

scholarly journals Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8

2020 ◽  
Vol 90 (327) ◽  
pp. 379-388
Author(s):  
V. Flammang
Keyword(s):  
Upper Bounds ◽  
Algebraic Integers ◽  
Totally Positive

scholarly journals On the Zhang–Zagier measure

2018 ◽  
Vol 14 (10) ◽  
pp. 2663-2671
Author(s):  
V. Flammang
Keyword(s):  
Lower Bound ◽  
Mahler Measure ◽  
Algebraic Integers ◽  
Totally Positive ◽  
The Absolute

We first improve the known lower bound for the absolute Zhang–Zagier measure in the general case. Then we restrict our study to totally positive algebraic integers. In this case, we are able to find six points for the related spectrum. At last, we give inequalities involving the Zhang–Zagier measure, the Mahler measure and the length of such integers.

Totally positive algebraic integers with small trace

2021 ◽  
pp. 1
Author(s):  
Cong Wang ◽  
Jie Wu ◽  
Qiang Wu
Keyword(s):  
Algebraic Integers ◽  
Totally Positive

scholarly journals The trace of totally positive algebraic integers

2005 ◽  
Vol 75 (253) ◽  
pp. 385-394 ◽  
Author(s):  
Julián Aguirre ◽  
Mikel Bilbao ◽  
Juan Carlos Peral
Keyword(s):  
Algebraic Integers ◽  
Totally Positive

scholarly journals The ${\rm R}_2$ measure for totally positive algebraic integers

2016 ◽  
pp. 1-9
Author(s):  
V. Flammang
Keyword(s):  
Algebraic Integers ◽  
Totally Positive

scholarly journals The Mahler measure and its areal analog for totally positive algebraic integers

2015 ◽  
Vol 151 ◽  
pp. 211-222
Author(s):  
V. Flammang
Keyword(s):  
Mahler Measure ◽  
Algebraic Integers ◽  
Totally Positive

scholarly journals The absolute trace of totally positive reciprocal algebraic integers

2017 ◽  
Vol 170 ◽  
pp. 66-74 ◽  
Author(s):  
Xiaoqian Dong ◽  
Qiang Wu
Keyword(s):  
Algebraic Integers ◽  
Totally Positive ◽  
The Absolute

scholarly journals THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

2011 ◽  
Vol 90 (3) ◽  
pp. 341-354 ◽  
Author(s):  
YANHUA LIANG ◽  
QIANG WU
Keyword(s):  
Lower Bounds ◽  
Algebraic Integer ◽  
Algebraic Integers ◽  
Auxiliary Functions ◽  
Salem Numbers ◽  
Totally Positive

AbstractLet α be a totally positive algebraic integer of degree d≥2 and α1=α,α2,…,αd be all its conjugates. We use explicit auxiliary functions to improve the known lower bounds of Sk/d, where Sk=∑ di=1αki and k=1,2,3. These improvements have consequences for the search of Salem numbers with negative traces.

scholarly journals The measure of totally positive algebraic integers

2013 ◽  
Vol 133 (1) ◽  
pp. 12-19 ◽  
Author(s):  
Quanwu Mu ◽  
Qiang Wu
Keyword(s):  
Algebraic Integers ◽  
Totally Positive
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