The Smallest House Of Reciprocal Algebraic Integers

Let a be an algebraic integer of degree d.whose conjugates are α1=α.α2,…,αd,and with b0=1,bi∈ Z(i=1,2,…,d),its minimal polynomial.We denote,as usual,by the house of ca.If the minimal polynomial is reciprocal,i.e.P(x)=(1/x)xd,then the algebraic integer a is reciprocal.At present7people have found the smallest house of reciprocal algebraic integers of degree d<42.With the existing algorithms,we optimize the related auxiliary functions and improve the bound of Sk.We then obtain the smallest house of reciprocal algebraic integers of degree d=44.