The Trace of Totally Positive and Real Algebraic Integers

1945 ◽  
Vol 46 (2) ◽  
pp. 302 ◽  
Author(s):  
Carl Ludwig Siegel

2011 ◽  
Vol 80 (274) ◽  
pp. 1041-1041 ◽  
Author(s):  
James McKee




2018 ◽  
Vol 14 (10) ◽  
pp. 2663-2671
Author(s):  
V. Flammang

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.



2021 ◽  
pp. 1
Author(s):  
Cong Wang ◽  
Jie Wu ◽  
Qiang Wu


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






2017 ◽  
Vol 170 ◽  
pp. 66-74 ◽  
Author(s):  
Xiaoqian Dong ◽  
Qiang Wu


2011 ◽  
Vol 90 (3) ◽  
pp. 341-354 ◽  
Author(s):  
YANHUA LIANG ◽  
QIANG WU

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.



2013 ◽  
Vol 133 (1) ◽  
pp. 12-19 ◽  
Author(s):  
Quanwu Mu ◽  
Qiang Wu


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