Dirichlet series

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Vector Potential: Equations and Boundary Conditions

Explains vector potential equations and boundary conditions in detail.

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)

Euler Product and Perron's Formula

Explores the Euler product theorem and Perron's formula in number theory and complex analysis.

Fourier Series: Approximation and Convergence

Introduces Fourier series, explaining their approximation properties and convergence, along with the Dirichlet theorem and coefficient computation.

Untitled

Extreme Problems in Diophantine Approximation and Dynamics

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

Construction of Solutions by Dirichlet-Laplace

Explores the construction of solutions by Dirichlet-Laplace in general domains.

Untitled

Fourier Series: Dirichlet Theorem

Explores the Dirichlet theorem for deriving Fourier series of continuous functions.

Green Functions: Theory and Applications

Explores the theory and applications of Green functions in classical electrodynamics, emphasizing the importance of choosing the right function based on boundary conditions.