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On the arithmetic nature of definite integrals of rational functions.


Author: A. J. Van der Poorten
Journal: Proc. Amer. Math. Soc. 29 (1971), 451-456
MSC: Primary 10.32
DOI: https://doi.org/10.1090/S0002-9939-1971-0276180-X
MathSciNet review: 0276180
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Abstract: A. Baker's theorems on linear forms in the logarithms of algebraic numbers imply information on the arithmetic nature of definite integrals of rational functions. This paper pro vides a convenient formulation of these implied results.


References [Enhancements On Off] (What's this?)

  • [1] A. Baker, Linear forms in the logarithms of algebraic numbers. I-IV, Mathematika 13 (1966), 204-216; ibid. 14 (1967), 102-107, 220-228. MR 36 #3732. MR 0220680 (36:3732)
  • [2] K. Mahler, Lectures on a theorem of A. Baker, Report of the Tenth Summer Research Institute of the Australian Mathematical Society (Hobart, 1970).
  • [3] C. L. Siegel, Transcendental numbers, Ann. of Math. Studies, no. 16, Princeton Univ. Press, Princeton, N. J., 1949. MR 11, 330. MR 0032684 (11:330c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276180-X
Keywords: Linear form, algebraic number, transcendental number, rational function, definite integral, partial fraction expansion
Article copyright: © Copyright 1971 American Mathematical Society

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