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Short Report

ScienceAsia 24 (1998): 129-132 |doi: 10.2306/scienceasia1513-1874.1998.24.129

A P-ADIC LOWER BOUND FOR POLYNOMIAL EVALUATED AT AN ALGEBRAIC NUMBER

VICHIAN LAOHAKOSOL

ABSTRACT: Let F(x) be a polynomial with rational integral coefficients and let a be an algebraic number. A sharp lower bound for the p-adic valuation of nonzero F() is derived. The derivation, which makes use of a 1967 technique of R. Guting, gives a quantitative improvement of an old result of K. Mahler

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Department of Mathematics, Kasetsart University, Bangkok 10900, Thailand.

Received April 30, 1998