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Original scientific paper

Polynomial-exponential equations and linear recurrences

Clemens Fuchs

Fulltext: english, pdf (657 KB) pages 233-252 downloads: 57* cite
APA 6th Edition
Fuchs, C. (2003). Polynomial-exponential equations and linear recurrences. Glasnik matematički, 38 (2), 233-252. Retrieved from https://hrcak.srce.hr/1317
MLA 8th Edition
Fuchs, Clemens. "Polynomial-exponential equations and linear recurrences." Glasnik matematički, vol. 38, no. 2, 2003, pp. 233-252. https://hrcak.srce.hr/1317. Accessed 7 Dec. 2021.
Chicago 17th Edition
Fuchs, Clemens. "Polynomial-exponential equations and linear recurrences." Glasnik matematički 38, no. 2 (2003): 233-252. https://hrcak.srce.hr/1317
Harvard
Fuchs, C. (2003). 'Polynomial-exponential equations and linear recurrences', Glasnik matematički, 38(2), pp. 233-252. Available at: https://hrcak.srce.hr/1317 (Accessed 07 December 2021)
Vancouver
Fuchs C. Polynomial-exponential equations and linear recurrences. Glasnik matematički [Internet]. 2003 [cited 2021 December 07];38(2):233-252. Available from: https://hrcak.srce.hr/1317
IEEE
C. Fuchs, "Polynomial-exponential equations and linear recurrences", Glasnik matematički, vol.38, no. 2, pp. 233-252, 2003. [Online]. Available: https://hrcak.srce.hr/1317. [Accessed: 07 December 2021]

Abstracts
Let K be an algebraic number field and let (Gn) be a linear recurring sequence defined by

Gn = + P2(n) + ... + Pt(n) ,

where , , ... , 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) to calculate an upper bound for the number of solutions (n,x) under some additional assumptions.

Keywords
Polynomial-exponential equations; linear recurrences; Subspace-Theorem

Hrčak ID: 1317

URI
https://hrcak.srce.hr/1317

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