Lectures related to Proof of Explicit Formula

Prime Number Theorem

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

Prime Numbers: Euclid's Theorem

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

Logarithmic Derivative of Zeta

Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Modular Arithmetic: Foundations and Applications

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

Abel Summation and Prime Number Theory

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

Logarithmic Derivative of Zeta

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

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Prime Number Theorem

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

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

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.

Compact Sets and Convergence

Explains compact sets, convergence, and absolute convergence in real analysis.