Abstract
Explicit auxiliary functions can be used in the âSchur-Siegel- Smyth trace problemâ. In the previous works, these functions were constructed only with polynomials having all their roots positive. Here, we use several polynomials with complex roots, which are found with Wuâs algorithm, and we improve the known lower bounds for the absolute trace of totally positive algebraic integers. This improvement has a consequence for the search of Salem numbers that have a negative trace. The same method also gives a small improvement of the upper bound for the integer transfinite diameter of [0,1].
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