## Algebraic numbers close to both $0$ and $1$

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- Math. Comp.
**61**(1993), 485-491 Request permission

## Abstract:

A recent theorem of Zhang asserts that \[ H(\alpha ) + H(1 - \alpha ) \geq C\] for all algebraic numbers $\alpha \ne 0,1, (1 \pm \sqrt { - 3} )/2$, and some constant $C > 0$. An elementary proof of this, with a sharp value for the constant, is given (the optimal value of*C*is $\tfrac {1}{2}\log (\tfrac {1}{2}(1 + \sqrt 5 )) = 0,2406 \ldots$, attained for eight values of $\alpha$) and generalizations to other curves are discussed.

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## Additional Information

- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp.
**61**(1993), 485-491 - MSC: Primary 11R06; Secondary 11R04, 12D10
- DOI: https://doi.org/10.1090/S0025-5718-1993-1197513-9
- MathSciNet review: 1197513