Lectures related to Algebraic number theory

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Introduces the Abel summation formula and its application in establishing various equivalent formulations of the Prime Number Theory.

Applications of Ergodic Theory to Combinatorics

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Number Theory: Congruence

Covers congruence modulo m and arithmetic operations.

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.

Number Fields: Embeddings and Ideal Classes

Covers the embeddings of number fields and ideal classes with proofs and examples.

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Number Theory: Congruence

Explains congruence modulo m and its applications in arithmetic operations.

Rudiments of Number Theory

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

Number Theory: Division

Explores the concept of division in number theory, including properties, algorithms, and examples.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Logarithmic Derivative of Zeta

Explores the behavior of the zeta function and its explicit formula.

Number Theory: Prime Numbers and Modular Arithmetic

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Hadamard Factorization and Zeros of Zeta

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Cyclotomic Extensions: Norms, Ideals, and Primes

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

RSA Encryption: Main Concepts

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

Prime Numbers: Euclid's Theorem

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Logarithmic Embedding in Number Fields

Explores the properties and applications of logarithmic embeddings in number fields.

The Greatest Common Divisor

Covers the greatest common divisor, Euclidean algorithm, Joseph Stein's algorithm, and practical examples.