Abstract
We begin with some preliminaries on algebraic numbers. Let α be an algebraic number. Then we observe that α satisfies the polynomial of minimal degree such that it has relatively prime integer coefficients and the leading coefficient positive. This is the minimal polynomial of α. The degree of this polynomial is called the degree of α. The maximum of the absolute values of the coefficients of this polynomial is called the height of α. We write ν = ν(α) for the least positive integer such that να is an algebraic integer i.e., να satisfies a monic polynomial with integer coefficients. The integer ν exists and we say that it is the denominator of α.
This article is based on the lectures given at NBHM Instructional Conference on Elliptic Curves held at TIFR in 1991. This is a revised version of the lecture notes appeared in the last reference NBHM (1991) at the end.
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Shorey, T.N. (2003). Approximations of Algebraic Numbers by Rationals: A Theorem of Thue. In: Bhandari, A.K., Nagaraj, D.S., Ramakrishnan, B., Venkataramana, T.N. (eds) Elliptic Curves, Modular Forms and Cryptography. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-15-6_9
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DOI: https://doi.org/10.1007/978-93-86279-15-6_9
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