Additive Relations in Fields: An Entropy Approach

Tom Ward

Research output: Contribution to journalArticlepeer-review


Let x1,...,xr be complex numbers with K = Q(x1,...,xr) 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 Î G = . 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.
Original languageEnglish
Pages (from-to)137-143
Number of pages7
JournalJournal of Number Theory
Issue number1
Publication statusPublished - 1995

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