Dirichlet Series: Analytic and Algebraic Properties

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Approximation of Zeta Function

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

Dirichlet Series: Properties and Examples

Explores the properties and examples of Dirichlet series, highlighting their key characteristics and applications.

Real Analytic Functions

Explores real analytic functions, discussing their convergence and neighborhood properties in different contexts.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

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.

Hadamard Factorization and Zeros of Zeta

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Logarithmic Derivative of Zeta

Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.

Riemann Integral: Convergence and Limit Process

Explores Riemann integral, convergence, and limit processes, emphasizing continuity and monotonic convergence.