Zeta function regularization

Related lectures (23)

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Explores the analytic continuation of the zeta function and its relation to holomorphic functions and natural numbers.

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

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

\psi(x)

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

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

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

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

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

Explores the analytic and algebraic properties of Dirichlet series associated with arithmetic functions.

Explores the path integral description of the quantum harmonic oscillator and its connection to prime numbers and the Riemann Zeta-function.