Functional Equation of Zeta and Hadamard Products

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Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Matricizations and Alternating Least Squares

Covers matricizations, ALS method, and tensor decomposition, emphasizing the alignment of fibers in matrices.

Proof of Explicit Formula

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

Generalized Integrals: Convergence and Divergence

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

Logarithmic Derivative of Zeta

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

Two-loop Computations: External Legs and Internal Propagators

Covers the computation of two-loop diagrams with external legs and internal propagators.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.