Stirling's Formula and Functional Equation for Zeta

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

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

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

Illustrates the resolution of a linear equation with a second member.

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

\psi(x)

Explores the convergence of a series parameterized by alpha and its conditions for convergence.

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

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

Explores Stirling's formula applications, polarization in vectors, and graph embeddings in Euclidean space.

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

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