Linear Equations over Multiplicative Groups , Recurrences , and Mixing I
نویسندگان
چکیده
Let K be a field of positive characteristic. When V is a linear variety in K and G is a finitely generated subgroup of K∗, we show how to compute the set V ∩ G effectively using heights. We calculate all the estimates explicitly. A special case provides the effective solution of the S-unit equation in n variables. 2000 MSC codes. 11D04, 11D72, 11G35, 11G50, 14G25.
منابع مشابه
Linear Equations over Multiplicative Groups, Recurrences, and Mixing II
Let u1, . . . , um be linear recurrences with values in a field K of positive characteristic p. We show that the set of integer vectors (k1, . . . , km) such that u1(k1) + · · ·+ um(km) = 0 is p-normal in a natural sense generalizing that of the first author, who proved the result for m = 1. Furthermore the set is effectively computable if K is. We illustrate this with an example for m = 4. We ...
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