Concept

Analytic number theory

Related lectures (31)

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.

Effective Version of the Explicit Formula

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

Proof of Explicit Formula

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

Local Zeta Functions

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

Abel Summation and Prime Number Theory

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

Multicorrelation Sequences and Primes

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

Complex Numbers: Group Morphisms and Fermat Primes

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

Logarithmic Derivative of Zeta

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

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 Theory: Congruence

Explains congruence modulo m and its applications in arithmetic operations.

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.

Algebraic Structures: Groups and Rings

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

Number Theory: Prime Numbers and Modular Arithmetic

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

Prime Number Theorem

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

Fermat's Little Theorem: Applications and Probabilities

Explores Fermat's Little Theorem applications and probabilities in primality testing.

Euler Product and Perron's Formula

Explores the Euler product theorem and Perron's formula in number theory and complex analysis.

Rudiments of Number Theory

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

Number Theory: History and Concepts

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

Prime Numbers: Euclid's Theorem

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

Fermat's Little Theorem

Explores Fermat's Little Theorem, its extensions, primality testing algorithms, and the significance of prime numbers in cryptography.