The Number of Solutions of Polynomial-Exponential Equations

2000/01/01 by H. P. Schlickewei, Hans Peter Schlickewei, Wolfgang Schmidt +1 · 45 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Applied mathematics #Differential equation #Exponential dichotomy #Exponential function #Exponential polynomial #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Polynomial #Pure mathematics

paper · pdf · doi:10.1023/a:1001719425893

published in Compositio Mathematica 120(2), 193-225 (Cambridge University Press)

openalex publication_date 2000/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

We will give explicit bounds for the number of solutions of polynomial-exponential equations. In contrast to earlier work, the bounds are independent of the coefficients of the equations, and they are of only single exponential growth in the number of coefficients.

Citations

• Linear Equations in Variables which Lie in a Multiplicative Group

Cited by

• On numbers n dividing the nth term of a linear recurrence
• Decidability of multiplicative matrix equations and related Diophantine problems
• A Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata

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