Additive Relations in Fields: An Entropy Approach

Ward, Tom (1995) Additive Relations in Fields: An Entropy Approach. Journal of Number Theory, 53 (1). pp. 137-143.

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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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 03 Oct 2022 04:45
DOI: 10.1006/jnth.1995.1082

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