Concept

Dirichlet's theorem on arithmetic progressions

Related lectures (19)

Dirichlet Characters: Definition and Properties

Explores Dirichlet characters, covering their definition, periodicity, and properties through a mock exam.

Introduces characters over a finite abelian group and explains the proof of the infinitude of primes in arithmetic progressions.

Prime Number Theorem

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

Number Theory: More Facts about Primes

Explores distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Number Theory: History and Concepts

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Rudiments of Number Theory

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

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Modulo: Congruence and Check Digits

Explores modulo arithmetic rules and check digits for data accuracy.

Prime Number Theorem

Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.

Mertens' Theorems and Mobius Function

Explores Mertens' theorems on prime estimates and the behavior of the Mobius function in relation to the prime number theorem.

The Riemann Hypothesis

Explores the Riemann Hypothesis, prime numbers, Zeta-function, and quantum mechanics.

Abel Summation and Prime 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.

Abel Summation: Analyzing Logarithmic Functions

Explores Abel summation formula, Chebyshev's theorem, and logarithmic functions with practical examples.

Number Theory: More Facts about Primes

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

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.

Quantifier Free Formula

Covers the transformation of quantifier free formulas into equisatisfiable formulas and reduction to solve modulo arithmetic.

Sequences: Definitions and Examples

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.