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Polynomial – Exponential Equations and Linear Recurrences
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fuchs, Clemens |
| Abstract | Let K be an algebraic number field and let (Gn) be a linear recurring sequence defined by Gn = λ1α1 +P2(n)α n 2 +· · ·+Pt(n)α n t , where λ1, α1, . . . , αt are non-zero elements of K and where Pi(x) ∈ K[x] for i = 2, . . . , t. Furthermore let f(z, x) ∈ K[z, x] monic in x. In this paper we want to study the polynomial–exponential Diophantine equation f(Gn, x) = 0. We want to use a quantitative version of W. M. Schmidt’s Subspace Theorem (due to J.-H. Evertse [8]) to calculate an upper bound for the number of solutions (n, x) under some additional assumptions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://web.math.pmf.unizg.hr/glasnik/38.2/38(2)-03.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Emoticon Linear algebra Linear logic Monic polynomial Recurrence (disease attribute) Recurrence relation Schmidt decomposition Solutions exponential |
| Content Type | Text |
| Resource Type | Article |
