Re: multiplicative vs algebraic independence

From: Roberto E. Martinez II (remartin_at_fas.harvard.edu)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 15:30:03 +0000 (UTC)

All:

Thanks for the reply. You are correct; I left a bit out:

Let d1,d2,...,dn be complex numbers, linearly independent over the
rationals. The functions

exp(d1 t), exp(d2 t), ..., exp(d3 t)

are algebraically independent over the complex numbers. If we denote
these functions x1,x2,...,xn, then we note that they are
multiplicatively independent and satisfy no relation of the form

x1^b1 x2^b2 ... xn^bn = 1

for positive integers b1,b2,...,bn not all zero. From this (according
to Lang) it follows that they are algebraically independent, too.

Best,
Roberto

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