LAUSR

Abstract The house of an algebraic integer of degree d is the largest modulus of its conjugates. In this work, we compute the smallest houses m r ( d ) of all reciprocal algebraic integers for degree 28 ≤ d ≤ 42 , and we suggest that m r ( d ) ≥ m r ( 20 ) 20 / d . In our computations, we use a family of explicit auxiliary function using the properties of reciprocal algebraic integer which give better bounds for S k than the last one.