MATH-603: Subconvexity, Periods and Equidistribution

Lectures in this course (35)

Covers the concept of characters and moduli in mathematics.

Covers the representation theory of groups, focusing on actions and invariants.

Covers the decomposition of Eisenstein series into orthogonal components and the unitarizability of certain representations.

Covers Eisenstein series properties and spectral decomposition of functions.

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Covers the spherical Hecke algebra and finite-dimensional unitary representations.

Explores Principal Series representations in mathematics, unitary properties, eigenvalues, and Satake parameter.

Covers vector spaces, interpolation, conductor, and correspondence in local irreducible representations.

Discusses Fourier expansion, quaternion algebra, and Whittaker model in automorphic forms.

Covers the properties of the Whittaker model and its analytic continuation.

Covers the rapid decay of Whittaker functions for upsets, focusing on the assumption of Vize = 1.

Covers the Fourier expansion of modular forms and the Rankin-Selberg method.

Covers quaternion algebra, Waldspurger formula, and Hermite space in relation to L-functions and inner products.

Covers the equidistribution of representations of integers by ternary forms and the conductor of X.

Explores the approximation of the zeta function using compact functions and spectral decomposition.

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