A Diophantine approach to the three and four exponentials conjectures

Lee A Butler

doi:10.1007/s11139-015-9728-2

A Diophantine approach to the three and four exponentials conjectures

Lee A Butler

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Abstract

Some special cases of Wilkie's conjecture are shown to be equivalent to real versions of the three and four exponentials conjectures. Wilkie's conjecture is an open problem originating in model theory that concerns the density of algebraic points in sets defined using the exponential function; the latter conjectures concern the algebraic nature of values of the exponential function.

Original language	English
Pages (from-to)	199-221
Number of pages	23
Journal	Ramanujan Journal
Volume	42
Issue number	1
Early online date	13 Oct 2015
DOIs	https://doi.org/10.1007/s11139-015-9728-2
Publication status	Published - 1 Jan 2017

Keywords

transcendence
exponential function
logarithms of algebraic numbers
algebraic independence

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10.1007/s11139-015-9728-2

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AB - Some special cases of Wilkie's conjecture are shown to be equivalent to real versions of the three and four exponentials conjectures. Wilkie's conjecture is an open problem originating in model theory that concerns the density of algebraic points in sets defined using the exponential function; the latter conjectures concern the algebraic nature of values of the exponential function.

KW - transcendence

KW - exponential function

KW - logarithms of algebraic numbers

KW - algebraic independence

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EP - 221

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A Diophantine approach to the three and four exponentials conjectures

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