Lectures related to Number theory

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with 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: Division, Remainder, Congruence

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Number Theory: Congruence

Covers congruence modulo m and arithmetic operations.

Prime Numbers: Euclid's Theorem

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

Effective Version of the Explicit Formula

Explores the effective version of the explicit formula in Number Theory, focusing on smooth functions and integral calculations.

Complex Numbers: Group Morphisms and Fermat Primes

Explores group morphisms in complex numbers and the concept of Fermat primes.

Cyclotomic Extensions: Norms, Ideals, and Primes

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

Abel Summation and Prime Number Theory

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

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

Number Theory: Division

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

Number Theory: Prime Numbers and Modular Arithmetic

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

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.

Rudiments of Number Theory

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

Local Zeta Functions

Covers the classification of comport p-adic fields using integration and Igusa's local zeta functions.

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.