Riemann zeta function

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Related lectures (32)

Page 3 of 4

The Riemann Hypothesis

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

Classical Zero Free Region for Zeta and Explicit Formula I

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

\psi(x)

Double Integrals: Definitions and Properties

Covers the definitions and properties of double integrals over compact regions.

Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Approximation of Zeta Function

Explores the approximation of the zeta function using compact functions and spectral decomposition.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Definite Integral: Riemann Sum

Introduces Riemann sums as approximations of the area under a function's graph.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

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.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.