Polynomial–exponential equations and Zilber's conjecture

DOI10.1112/blms/bdv096zbMath1347.11036arXiv1402.0685OpenAlexW3105564543WikidataQ59894393 ScholiaQ59894393MaRDI QIDQ2801725

Vincenzo Mantova

Publication date: 21 April 2016

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0685

zbMATH Keywords

Schanuel's conjecturetranscendental solutionspolynomial-exponential equationHermite-Lindemann-Weierstraß theoremZilber's strong exponential closedness

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Exponential Diophantine equations (11D61) Model theory (number-theoretic aspects) (11U09)

Related Items (6)

Pseudo-exponential maps, variants, and quasiminimality ⋮ Generic solutions of equations with iterated exponentials ⋮ Exponential sums equations and tropical geometry ⋮ A closure operator respecting the modular \(j\)-function ⋮ A weak version of the strong exponential closure ⋮ Solutions of equations involving the modular 𝑗 function

Cites Work

• Pseudo-exponentiation on algebraically closed fields of characteristic zero
• Équations exponentielles-polynômes et suites récurrentes linéaires. II. (Exponential polynomial equations and linear recurrence sequences. II)
• On the integer solutions of exponential equations in function fields.
• RATIONAL SOLUTIONS OF POLYNOMIAL-EXPONENTIAL EQUATIONS
• A remark on Zilber's pseudoexponentiation
• Linear forms in the logarithms of algebraic numbers
• Linear forms in the logarithms of algebraic numbers (II)
• Linear forms in the logarithms of algebraic numbers (III)

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