Totally Real Integral Points on a Plane Algebraic Curve


Michel LAURENT Abstract. Let F (X,Y ) = ∑m i=0 ∑n j=0 ai,jX iY j be an absolutely irreducible polynomial in Z[X,Y ]. Suppose that m ≥ 1, n ≥ 2 and that the polynomial ∑n j=0 am,jY j is reducible in Q[Y ], has n simple roots and an unique real root. Let L be a totally real number field and let (ξ, ζ) ∈ OL ×L be such that F (ξ, ζ) = 0. We give an upper bound… (More)