A Diophantine approach to the three and four exponentials conjectures

作者：Butler Lee A^*

来源：Ramanujan Journal, 2017, 42(1): 199-221.

DOI：10.1007/s11139-015-9728-2

• Transcendence
• Exponential function
• Logarithms of algebraic numbers
• Algebraic independence

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.

• 出版日期2017-1