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These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Commentaire
From the reviews:
"This set of lectures originates from an introductory course given by the author at the Scuola Normale Superiore Pisa in 2006-2007 on Diophantine analysis. ... provide a lot of further information on these topics, including recent developments and open problem. Hence this booklet starts at an elementary level ... and reaches the limit of our current knowledge on all these topics. ... a useful addition to the literature on this fashionable topic, both for the beginner and for the researcher." (Michel Waldschmidt, Zentralblatt MATH, Vol. 1186, 2010)
