On the integer solutions of exponential equations in function fields.

DOI10.5802/aif.2036zbMath1080.11028OpenAlexW2463569745MaRDI QIDQ1774047

Umberto Zannier

Publication date: 29 April 2005

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2004__54_4_849_0

zbMATH Keywords

function fieldsDiophantine equationsnumber of integer solutions\(S\)-unit type equationexponential equations in several variablesrecurrence of polynomials

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61) Diophantine equations (11D99)

Related Items (9)

Effective bounds for the zeros of linear recurrences in function fields ⋮ Perfect powers in polynomial power sums ⋮ RATIONAL SOLUTIONS OF POLYNOMIAL-EXPONENTIAL EQUATIONS ⋮ Decomposable polynomials in second order linear recurrence sequences ⋮ PENCILS OF NORM FORM EQUATIONS AND A CONJECTURE OF THOMAS ⋮ On the Diophantine Equation G n (x) = G m (y) with Q (x, y)=0 ⋮ Polynomial–exponential equations and Zilber's conjecture ⋮ Composite values of polynomial power sums ⋮ Newton functions generating symmetric fields and irreducibility of Schur polynomials

Cites Work

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• Linear equations in variables which lie in a multiplicative group
• On Schanuel's conjectures
• Equations in one variable over function fields
• Vanishing sums in function fields
• On equations in two S-units over function fields of characteristic 0
• On the Diophantine equation 𝐺_{𝑛}(𝑥)=𝐺_{𝑚}(𝑃(𝑥)): Higher-order recurrences
• Some remarks on the S-unit equation in function fields

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