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Binary Quadratic Forms and the Ideal Class Group - math harvard

Binary Quadratic Forms and the Ideal Class Group - math harvard 2025

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The document explores the genus theory of Binary Quadratic Forms, focusing on the classification of ideals in quadratic fields and their connection to the ideal class group. It discusses equivalence relations among binary quadratic forms, Lagrange's theory of reduced forms, and provides an alternative proof of Fermat's theorem regarding primes represented as sums of two squares. The paper establishes a relationship between the ideal class group of number fields and the class group of binary quadratic forms, demonstrating that both are finite abelian groups.

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