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Auxiliary Polynomials in Number Theory by David Masser

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Introduction

Ever since it was invented, arguably by Runge, the method of auxiliary polynomials has been vital to (and of unreasonable effectiveness in) the modern development of key aspects of number theory. The aim of this book is to give an account of the method in many of its forms, focusing almost exclusively on those polynomials which cannot be written down explicitly.

I well remember (standing in Heffers bookshop Cambridge around 1970) reading about this method in the foreword to Lang’s book on transcendental numbers, and experiencing disbelief that anything so far-fetched could work at all. So I will not attempt any explanation at this point.

Instead, I (or from now on, the authorial we) treat the method as the union of its examples, ...

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