A note on algebraic independence of logarithmic and exponential constants

Authors:
B. F. Caviness;M. J. Prelle
Affiliations:
Rensselaer Polytechnic Institute, Troy, New York;Rensselaer Polytechnic Institute, Troy, New York
Venue:
ACM SIGSAM Bulletin
Year:
1978

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Abstract

This paper gives a corollary to Schanuel's conjecture that indicates when an exponential or logarithmic constant is transcendental over a given field of constants. The given field is presumed to have been built up by starting with the rationals Q with π adjoined and taking algebraic closure, adjoining values of the exponential function or of some fixed branch of the logarithmic function, and then repeating these two operations a finite number of times.