Lectures related to Number Fields: Embeddings and Ideal Classes

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

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Ramification Theory: Residual Fields and Discriminant Ideal

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

The classical Lie algebras

Covers the classical Lie algebras, focusing on calculations and dimensions.

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Cyclotomic Extensions: Norms, Ideals, and Primes

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.