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Zeros of linear recurrence sequences |
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| Authors: | Hans Peter Schlickewei Wolfgang M. Schmidt Michel Waldschmidt | |
| Affiliation: | Fachbereich Mathematik, Universit?t Marburg, Hans-Meerwein-Strasse, Lahnberge, D-35032 Marburg, Germany.?e-mail: hps@mathematik.Uni-Marburg.de, DE Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO 80309-0395, USA. e-mail: schmidt@euclid.colorado.edu, US Université P. et M. Curie (Paris VI), Institut Mathématique de Jussieu, Problèmes Diophantiens, Case 247, 4, Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: miw@math.jussieu.fr, FR |
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| Abstract: | Let be an exponential polynomial over a field of zero characteristic. Assume that for each pair i,j with i≠j, α i /α j is not a root of unity. Define . We introduce a partition of into subsets (1≤i≤m), which induces a decomposition of f into , so that, for 1≤i≤m, , while for , the number either is transcendental or else is algebraic with not too small a height. Then we show that for all but at most solutions x∈ℤ of f(x)= 0, we have |
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| Keywords: | Mathematics Subject Classification (1991):11B37 11D61 11J13 | |
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