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Related lectures (28)

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

RSA Cryptography: Primality Testing and Quadratic Residues

Explores RSA cryptography, covering primality testing, quadratic residues, and cryptographic applications.

Arithmetic functions

Covers the analysis of arithmetic functions, including prime numbers and the Riemann hypothesis.

Prime Gaps and Multiplicative Sieve Inequalities

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

Arithmetic Functions: Multiplicative Functions and Dirichlet Convolution

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

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.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Petersson Inner Product and Hecke Operators

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

Legendre and Jacobi Symbols: RSA Cryptography

Explores Legendre and Jacobi symbols, quadratic residuosity, element orders, and RSA Cryptography complexities.

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.

Integers: Sets, Maps, and Principles

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

The Riemann Hypothesis

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

Integer Factorization: Quadratic Sieve

Covers the Quadratic Sieve method for integer factorization, emphasizing the importance of choosing the right parameters for efficient factorization.

Euler product and Perron's formula

Introduces the Euler product and Perron's formula in arithmetic functions.

Fermat's Little Theorem

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

Primes: Fundamental Theorem and Sieve of Eratosthenes

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.

Modular Forms: Properties and Applications

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Prime Numbers: Finding and Testing

Covers the definition of a function to determine if a given number is prime.

Prime Number Theorem

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

Dirichlet Series: Analytic and Algebraic Properties

Explores the analytic and algebraic properties of Dirichlet series associated with arithmetic functions.

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