Conductor of X: Waldsparger Formula and Subconvexity Bound

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Explores quadratic spaces, norms, and quaternion algebra over fields.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Covers the definition and properties of matrix norms and the exponential of matrices.

Explores symmetric matrices, diagonalization, and orthogonality properties, emphasizing simplicity and geometric relationships.

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.

Covers strategies for matrix operations and the concept of vector spaces.

Covers the basics of linear algebra, focusing on solving systems of linear equations through operations to triangular form.