| A Perron number α is a real algebraic integer with degree d ≥ 2,whose conjugates are αi,such that α>(?)|α_i|.For the smallest Perron number,there is a famous conjecture of Lind-Boyd[9]:Conjecture(Lind-Boyd).The smallest Perron number of degree d≥ 2 has minimal polynomialThis conjecture was studied by many people for many years.All the smallest Perron number of degree d<25 satisfy this conjecture.In our work,we improve the algorithm for computing the upper and lower bounds of S_k,we then have the smallest Perron number of degree d = 26,27,and verified this Perron number satisfies the conjecture of Lind-Boyd. |
