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15 September 2016 Ax–Schanuel for the j-function
Jonathan Pila, Jacob Tsimerman
Duke Math. J. 165(13): 2587-2605 (15 September 2016). 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.

Citation

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Jonathan Pila. Jacob Tsimerman. "Ax–Schanuel for the j-function." Duke Math. J. 165 (13) 2587 - 2605, 15 September 2016. https://doi.org/10.1215/00127094-3620005

Information

Received: 21 January 2015; Revised: 28 September 2015; Published: 15 September 2016
First available in Project Euclid: 10 June 2016

zbMATH: 06650079
MathSciNet: MR3546969
Digital Object Identifier: 10.1215/00127094-3620005

Subjects:
Primary: 11C18
Secondary: 03C98

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 13 • 15 September 2016
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