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Concept

Analytic number theory

Related lectures (31)

Primes in Arithmetic Progression Log in to Mediaspace to watch this video

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.

Hadamard Factorization and Zeros of Zeta Log in to Mediaspace to watch this video

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 Log in to Mediaspace to watch this video

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

Prime Number Theorem Log in to Mediaspace to watch this video

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

Euler Product and Perron's Formula Log in to Mediaspace to watch this video

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

Dirichlet Characters: Definition and Properties Log in to Mediaspace to watch this video

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

Cyclotomic Extensions: Norms, Ideals, and Primes Log in to Mediaspace to watch this video

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

Number Theory: Operations and Equivalence Log in to Mediaspace to watch this video

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

Arithmetic Functions: Multiplicative Functions and Dirichlet Convolution Log in to Mediaspace to watch this video

Covers multiplicative functions, Dirichlet convolution, and the Mobius function in arithmetic functions.

Frobenius Theorems in Number Theory Log in to Mediaspace to watch this video

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Fermat's Equation: Integral Solutions and Gaussian Integers Log in to Mediaspace to watch this video

Discusses Fermat's equation and Gaussian integers' properties.