An analog to the Schur-Siegel-Smyth trace problem
Résumé
If α denotes a totally positive algebraic integer of degree d i.e., its conjugates α 1 = α,. .. , α d are positive real numbers, we define S k (α) = d i=1 α k i. S 1 (α) is the usual trace of α and was studied by many authors throughout the years. In this paper, we focus our attention on the values of S 2 (α) and our purpose is to establish for S 2 the same kind of results than for the trace.
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