Ax-Schanuel type theorems on functional transcendence via Nevanlinna theory

DOI10.1007/s00209-021-02848-xzbMath1487.32083arXiv1909.01018OpenAlexW3196902913WikidataQ113906060 ScholiaQ113906060MaRDI QIDQ2069644

Jiaxing Huang, Tuen-Wai Ng

Publication date: 21 January 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01018

zbMATH Keywords

Nevanlinna theoryAx-Schanuel theoremfunctional transcendence

Mathematics Subject Classification ID

Value distribution theory in higher dimensions (32H30) Algebraic dependence theorems (32J10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The hyperbolic Ax-Lindemann-Weierstraß conjecture
• Ax-Schanuel for the \(j\)-function
• \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\)
• Diophantine problems and \(p\)-adic period mappings
• Rational points in periodic analytic sets and the Manin-Mumford conjecture
• On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane
• The theory of the exponential differential equations of semiabelian varieties
• Courbes sur une variété abélienne et points de torsion
• Some results on hypertranscendental meromorphic functions
• On factorization of entire functions
• Nevanlinna theory and complex differential equations
• The lemma of the logarithmic derivative in several complex variables
• The André-Oort conjecture for \(\mathcal A_g\)
• Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz
• Hypertranscendency of perturbations of hypertranscendental functions
• Functional transcendence for the unipotent Albanese map
• Ax-Schanuel for Shimura varieties
• Logarithmic difference lemma in several complex variables and partial difference equations
• The Ax-Schanuel conjecture for variations of Hodge structures
• On Schanuel's conjectures
• Difference analogue of the lemma on the logarithmic derivative with applications to difference equations
• O-minimality and certain atypical intersections
• Applications of the hyperbolic Ax–Schanuel conjecture
• IMPRIMITIVE PARAMETRIZATION OF ANALYTIC CURVES AND FACTORIZATIONS OF ENTIRE FUNCTIONS
• Some results on the Gamma function and other hypertranscendental functions
• The algebraic independence of Weierstrass functions and some related numbers
• A note on wronskians and linear dependence of entire functions in
• On composition of meromorphic functions in several complex variables
• On reduction of functional-differential equations
• A reduction of a type of functional-differential equation
• Nevanlinna Theory and Its Relation to Diophantine Approximation
• Hypertranscendence and linear difference equations
• Studies of Differences from the point of view of Nevanlinna Theory
• Mixed Ax–Schanuel for the universal abelian varieties and some applications
• Abstract Differential Algebra and the Analytic Case
• Some Topics in Differential Algebraic Geometry I: Analytic Subgroups of Algebraic Groups
• Meromorphic and algebroidal solutions of functional equations

This page was built for publication: Ax-Schanuel type theorems on functional transcendence via Nevanlinna theory