EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE

2002/02/01 by BORIS ZILBER, Boris Zilber · 10 citations
Mathematics · #History and Theory of Mathematics #Mathematics and Applications #Advanced Mathematical Identities

paper · doi:10.1112/s0024610701002861

Abstract

A uniform version of the Schanuel conjecture is discussed that has some model-theoretical motivation. This conjecture is assumed, and it is proved that any ‘non-obviously-contradictory’ system of equations in the form of exponential sums with real exponents has a solution.

Cited by

• Torsion points on families of squares of elliptic curves
• Weak modular Zilber–Pink with derivatives
• Singular intersections of subgroups and character varieties
• Arithmetic unlikely intersections in powers of the multiplicative group
• Ax–Schanuel for the j-function
• Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points
• Hodge loci and atypical intersections: conjectures
• Analytic and pseudo-analytic structures (a survey)
• Natural models of theories of green points
• On the Skolem Problem for Continuous Linear Dynamical Systems

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• The theory of exponential sums
• Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials
• From Schanuel's Conjecture to Shapiro's Conjecture
• Generic solutions of equations with iterated exponentials
• Some interesting number theory problems