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An application of Jensen's formula to polynomials
In this note new proofs will be given for two inequalities on polynomials due to N. I. Feldman [1] and A. 0. Gelfond [2], respectively; these inequalities are of importance in the theory of
An unsolved problem on the powers of 3/2
  • K. Mahler
  • Mathematics
    Journal of the Australian Mathematical Society
  • 1 May 1968
Let α be an arbitrary positive number. For every integer n ≦ 0 we can write where is the largest integer not greater than, i.e the integral part of, and rn is its fractional part and so satisfies the
Some suggestions for further research
  • K. Mahler
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1 February 1984
1. A problem on Liouville numbers Long ago, Mai I let [9] proved that if X is a Liouville number, and f{z) is a rational function with rational coefficients, then also f[X) is a Liouville number.
On a Theorem of Liouville in Fields of Positive Characteristic
  • K. Mahler
  • Mathematics
    Canadian Journal of Mathematics
  • 1 August 1949
A classical theorem of J. Liouville states that if z is a real algebraic number of degree n ≥ 2, then there exists a constant c > 0 such that for every pair of integers a, b with b ≠ 0.
An Interpolation Series for Continuous Functions of a p-adic Variable.
The theory of analytic functions of a p-adic variable (i. e. of functions defined by power series) is much simpler than that of complex analytic funktions and offers few surprises. On the other band,
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