Rational approximations to the dilogarithm

  title={Rational approximations to the dilogarithm},
  author={Masayoshi Hata},
  journal={Transactions of the American Mathematical Society},
  • M. Hata
  • Published 1993
  • Mathematics
  • Transactions of the American Mathematical Society
The irrationality proof of the values of the dilogarithmic function L 2 (z) at rational points z = 1/k for every integer k ∈ (−∞, −5] ∪ [7, ∞) is given. To show this we develop the method of Pade-type approximations using Legendre-type polynomials, which also derives good irrationality measures of L 2 (1/k). Moreover, the linear independence over Q of the numbers 1, log(1 − 1/k), and L 2 (1/k) is also obtained for each integer k ∈ (−∞, −5] ∪ [7, ∞) 

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