Abstract
Let α ≠ 1 be an algebraic number with relatively small height. Recently, many authors, including Amoroso, Dubickas, Mignotte and Waldschmidt, stated sharp lower bounds for the quantity |α − 1|. Here, we provide a p-adic analogue of their results. For instance, we give an upper bound for the absolute value of the norm of α − 1, and we show that our estimate is rather sharp in terms of the degree of α. Further, we discuss a generalization in several variables of our result.
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References
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Bugeaud, Y. Algebraic Numbers Close to 1 in Non-Archimedean Metrics. The Ramanujan Journal 2, 449–457 (1998). https://doi.org/10.1023/A:1009728826119
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DOI: https://doi.org/10.1023/A:1009728826119