Ax–Schanuel for the j-function

2016/06/10 by Jonathan Pila, Jacob Tsimerman · 6 citations
Mathematics · Computer Science · #Advanced Mathematical Identities #Advanced Topology and Set Theory #Polynomial and algebraic computation

paper · pdf · doi:10.1215/00127094-3620005

Abstract

In this paper we prove a functional transcendence statement for the j-function which is an analogue of the Ax–Schanuel theorem for the exponential function. It asserts, roughly, that atypical algebraic relations among functions and their compositions with the j-function are governed by modular relations.

Citations

• On the real exponential field with restricted analytic functions
• EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE

Cited by

• Bialgebraic varieties of the Gamma function
• Mixed Ax-Schanuel for the universal abelian varieties and some applications
• Modular Zilber-Pink for geometrically generic varieties
• A differential approach to Ax-Schanuel, I
• Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results
• Singular intersections in families of abelian varieties

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