Lectures related to Non-vanishing of Dirichlet L-function and Gamma functions

Primes in arithmetic progressions (II), and Gamma functions

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

Stirling's Formula and Functional Equation for Zeta

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Elementary Algebra: Numeric Sets

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

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.

Prime Numbers and Primality Testing

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

Prime Numbers: Euclid's Theorem

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

Analytical Extension of Gamma Function

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

Prime Number Theorem

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

Bessel Equation: First Frobenius Series Solution around x=0

Explores the Bessel equation solution method and the gamma function properties.

Prime Gaps and Multiplicative Sieve Inequalities

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

Gamma Function and Stirling's Approximation: Mathematical Methods

Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.

Chinese Remainders & RSA

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Number Theory: Fundamental Concepts

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

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.

Cyclotomic Extensions: Norms, Ideals, and Primes

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

Gamma function II, and Poisson summation formula

Covers the Gamma function properties and the Poisson summation formula for real and complex numbers.

Number Theory: Prime Numbers and Modular Arithmetic

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

Prime Numbers: Deterministic Approaches

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Number Theory: Division, Remainder, Congruence

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

Number Theory: History and Concepts

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