Lectures related to Prime Gaps and Multiplicative Sieve Inequalities

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

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

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

Arithmetic Functions: Multiplicative Functions and Dirichlet Convolution

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

Number Theory: History and Concepts

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

Abel Summation and Prime Number Theory

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

Arithmetic functions

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Prime Numbers and Primality Testing

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

Prime Number Theorem

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

Elementary Algebra: Numeric Sets

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

Prime Numbers: Euclid's Theorem

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

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Dirichlet Characters: Definition and Properties

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

Number Theory: Division, Remainder, Congruence

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

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.

Euler product and Perron's formula

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

Cyclotomic Extensions: Norms, Ideals, and Primes

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