Dedekind zeta function

Related lectures (32)

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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 solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

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

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

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

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

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