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Analytic proof of the Lindemann theorem

1952
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Pacific Journal of Mathematics
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1) ae a + be β + ... + se σ = 0 would be true if all coefficients a, b, , s were zero; it could be true with nonzero coefficients if any two exponents were equal; and it could be true, with nonzero coefficients and unequal exponents, if either the one or the other were transcendental. Thus 1 + e ιπ -0, and e (e) -e 2 = 0. Now, the Lindemann theorem says that the equation can be true in these cases only: LiNDEMANN THEOREM. The number e cannot satisfy an equation of the form (1), in which at

doi:10.2140/pjm.1952.2.231
fatcat:huznh4qwcfcbrcuiiwvnbmt3xe