Ax-Schanuel and exceptional integrability

Jonathan Pila; Jacob Tsimerman

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arXiv · 2202.04023

Ax-Schanuel and exceptional integrability

Jonathan Pila·Jacob Tsimerman

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Abstract

When can a primitive of a given algebraic function be con-structed by iteratively solving algebraic equations and composing withthe primitives of some other given algebraic functions or their inverses? We establish some results in this direction. Specifically, we establishdecision procedures for determining whether a given primitive can beexpressed in terms of finitely many others, or in terms of elliptic integrals.

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Jonathan Pila, Jacob Tsimerman. 2022-02-08. Ax-Schanuel and exceptional integrability. https://arxiv.org/abs/2202.04023

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