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On the number of zeros of exponential polynomials and related questions

Published online by Cambridge University Press:  17 April 2009

A.J. van der Poorten  and
I.E. Shparlinski
A.J. van der Poorten
Affiliation:
Centre for Number Theory Research, Macquarie University, NSW 2109, Australia, alf@macadam.mpce.mq.edu.au
I.E. Shparlinski
Affiliation:
Mosfilmovskaja Str dom 2 kv 41, Moscoe 119285, Russia
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Abstract

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We apply Straßmann's theorem to p–adic power series satisfying linear differential equations with polynomial coefficients and note that our approach leads to our estimating the number of integer zeros of polynomials on a given interval and thence to an investigation of the number of p–adic small values of a function on such an interval, that is, of the number of solutions of a congruence modulo pr.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 401 - 412
Copyright
Copyright © Australian Mathematical Society 1992

References

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