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An Easy Transcendence Measure for e
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The object of this note is to give a simple proof of the following theorem.
Theorem 1. Let n≥1 and a0,a1, ..., an be integers of which an≠0 and max|a1|≤H where H exceeds a constant Ho(n) depending only on n. Then
|a0+a1e+...+anen|≥H-cn
where C is an absolute constant.
Theorem 1. Let n≥1 and a0,a1, ..., an be integers of which an≠0 and max|a1|≤H where H exceeds a constant Ho(n) depending only on n. Then
|a0+a1e+...+anen|≥H-cn
where C is an absolute constant.
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