Exponential sums equations and tropical geometry
Abstract: Zilber’s Exponential-Algebraic Closedness Conjecture states that algebraic varieties in Cn×(C×)n intersect the graph of complex exponentiation, unless that contradicts the algebraic and transcendence properties of exp. We establish a case of the conjecture, showing that it holds for varieties which split as the product of a linear subspace of the additive group and an algebraic subvariety of the multiplicative group. This amounts to solving certain systems of exponential sums equations, and it generalizes old results of Zilber, which required the linear subspace to either be defined over a generic subfield of the real numbers, or it to be any subspace defined over the reals assuming unproved conjectures from Diophantine geometry and transcendence theory. The proofs use the theory of amoebas and tropical geometry
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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ISSN: 1420-9020
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2023
- Creator
- DOI
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10.1007/s00029-023-00853-y
- URN
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urn:nbn:de:bsz:25-freidok-2375391
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:47 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Gallinaro, Francesco Paolo
- Universität
Time of origin
- 2023
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