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Hermite interpolation and p-adic exponential polynomials

Published online by Cambridge University Press:  09 April 2009

A. J. van der Poorten
A. J. van der Poorten
Affiliation:
School of MathematicsThe University of New South Wales, Australia
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By employing a precise form of the Hermite interpolation formula we obtain a best possible bound for the number of zeros of p-adic exponential polynomials. As companion to this quantitative result we give a best possible bound on the coefficients, if the exponential polynomial is small at sufficiently many points.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1976 , pp. 12 - 26
Copyright
Copyright © Australian Mathematical Society 1976

References

Baker, A. (1971), ‘Recent advances in transcendence theory’, Proc. International Conference on Number Theory. Moscow, 09, 10, 67–69.Google Scholar
Baker, A. and Coates, J. (1975), ‘Fractional parts of powers of rationals’, Proc. Camb. Phil. Soc. 77, 269–279.CrossRefGoogle Scholar
Cijsouw, P. L. (1975), ‘On the simultaneous approximation of certain numbers’, Duke Math. J., 42, 249–257.CrossRefGoogle Scholar
Cijsouw, P. L. and Tijdeman, R. (1975), ‘An auxiliary result in the theory of transcendental numbers II’, Duke Math. J. 42, 239–247.CrossRefGoogle Scholar
Hayman, W. K., ‘Differential inequalities and local valency’, Pacific J. Math. 44, 117–137.CrossRefGoogle Scholar
Mahler, K. (1932), ‘Zur Approximation der Exponentialfunktion und des logarithmus’, J. reine und angew. Math., 166, 118–150.CrossRefGoogle Scholar
Mahler, K. (1935), ‘Über transzendente P-adische Zahlen’, Comp. Math. 2, 259–275.Google Scholar
Mahler, K. (1967a), ‘On a class of entire functions’, Acta. Math. Acad. Sci. Hungar. 18, 83–96.CrossRefGoogle Scholar
Mahler, K. (1967b), ‘Applications of some formulae by Hermite to the approximation of exponentials and logarithms’, Math. Annalen 168, 200–227.CrossRefGoogle Scholar
Schinzel, A. (1967), ‘Two theorems of Gelfond and some of their applications’, Acta Arith. 13, 177–236.Google Scholar
Shorey, T. N. (1972a), ‘Algebraic independence of certain numbers in the p-adic domain’, Indag. Math. 34, 423–435.CrossRefGoogle Scholar
Shorey, T. N. (1972b), ‘P-adic analogue of a theorem of Tijdeman and its application’, Indag. Math. 34, 436–442.CrossRefGoogle Scholar
Tijdeman, R. (1971), ‘On the number of zeros of general exponential polynomials’, Indag. Math. 33, 1–7.Google Scholar
Tijdeman, R. (1973), ‘An auxiliary result in the theory of transcendental numbers’, J. Numb. Theory 5, 80–94.CrossRefGoogle Scholar
van dèr Poorten, A. J. (1970), ‘Generalisations of Turán's main theorems on lower bounds for sums of powers’, Bull. Austral. Math. Soc. 2, 15–38.CrossRefGoogle Scholar
van der Poorten, A. J. (1975), ‘Some determinants that should be better known’, J. Austral. Math. Soc. 21, 278–288.Google Scholar
van der Poorten, A. J. (197?), ‘Zeros of p-adic exponential polynomials’, Indag. Math. (to appear).Google Scholar
Waldschmidt, M. (1974), Nombres Transcendants, Springer Lecture Notes 402.Google Scholar