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
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Anmerkungen
-
ISSN: 1420-9020
- Ereignis
-
Veröffentlichung
- (wo)
-
Freiburg
- (wer)
-
Universität
- (wann)
-
2023
- Urheber
- DOI
-
10.1007/s00029-023-00853-y
- URN
-
urn:nbn:de:bsz:25-freidok-2375391
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
14.08.2025, 10:51 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Gallinaro, Francesco Paolo
- Universität
Entstanden
- 2023
Ähnliche Objekte (12)
Exponential sums equations and tropical geometry
Twisted Kloosterman sums and cubic exponential sums
Exponential sums and finite groups
Exponential Equations
On the reconstruction of multivariate exponential sums
On a family of sparse exponential sums
On Discretizing Uniform Norms of Exponential Sums
Regular Polygonal Vortex Filament Evolution and Exponential Sums
Exponential sums in prime fields for modular forms
Tropical geometry
Elliptic curves, modular forms, and the associated exponential sums
The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
Exponential sums equations and tropical geometry
Twisted Kloosterman sums and cubic exponential sums
Exponential sums and finite groups
Exponential Equations
On the reconstruction of multivariate exponential sums
On a family of sparse exponential sums
On Discretizing Uniform Norms of Exponential Sums
Regular Polygonal Vortex Filament Evolution and Exponential Sums
Exponential sums in prime fields for modular forms
Tropical geometry
Elliptic curves, modular forms, and the associated exponential sums
The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
Exponential sums equations and tropical geometry
Twisted Kloosterman sums and cubic exponential sums
Exponential sums and finite groups
Exponential Equations
On the reconstruction of multivariate exponential sums
On a family of sparse exponential sums
On Discretizing Uniform Norms of Exponential Sums
Regular Polygonal Vortex Filament Evolution and Exponential Sums
Exponential sums in prime fields for modular forms
Tropical geometry
Elliptic curves, modular forms, and the associated exponential sums