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An Easy Transcendence Measure for e


Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India
     

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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.
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  • An Easy Transcendence Measure for e

Abstract Views: 229  |  PDF Views: 0

Authors

K. Ramachandra
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, India

Abstract


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.