Sums of squares, sums of cubes, and modern number theory
نویسنده
چکیده
These are notes which grew out of a talk for general math graduate students with the aim of starting from the questions “Which numbers are sums of two squares?” and “Which numbers are sums of two cubes?” and going on a tour of many central topics in modern number theory. In the notes, I discuss composition laws, class groups, L-functions, modular forms, and elliptic curves, ending with the Birch and SwinnertonDyer conjecture. The goal is not to explain any topic too deeply, but to provide some context for how these seemingly disparate topics piece together to (attempt to) satisfy the burning questions of classical number theory.
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تاریخ انتشار 2015