Lectures related to Logarithmic Derivative of Zeta

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

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

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

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

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

Establishes the classical zero free region for the Zeta function and starts the proof of the explicit formula for

\psi(x)

.

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

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

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Covers the statement of the Bernoulli's Hospital Rule and its application.

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Demonstrates the practical application of theorems in calculus through two clever examples.

Explores the properties and examples of Dirichlet series, highlighting their key characteristics and applications.

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