Additive Relations in Fields: an Entropy Approach
نویسندگان
چکیده
Let ξ1, . . . , ξr be complex numbers with K = Q(ξ1, . . . , ξr) having transcendence degree r − 1 over Q. Consider the equation a1x1 + · · ·+ akxk = 1, (1) in which the ai’s are fixed elements of K ×, no proper subsum ai1xi1 + · · ·+ aijxij vanishes, and we seek solutions xi ∈ Γ = ξ1, . . . , ξr . It is well–known that (1) has only finitely many solutions; we present here an elementary proof of this fact using results from the entropy theory of commuting group automorphisms.
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