Math 213b, Spring 2005

Professor Yum-Tong Siu
(511 Science Center,   Office Hours: MWF 11-12)

Meeting in Science Center 116, MWF 12

 

Lecture Notes: "Construction of Harmonic Functions with Singularities on Riemann Surfaces as Electrostatic Potentials"

Lecture Notes: "Construction of Meromorphic and Holomorphic Forms, Period Matrices, and Riemann Relations"

Lecture Notes: "The Theorem of Riemann-Roch and Abel's Theorem"

Lecture Notes: "The Proof of the Bieberbach Conjecture"

Lecture Notes: "Darboux's Proof of the Addition Theorem of Elliptic Functions by Conservation Law of a System of Two Pendulums"

Lecture Notes: "Overview of the Material on the Riemann Hypothesis to Be Covered in the Course"

Lecture Notes: "Proof of Functional Equation of Riemann Zeta Function by Contour Integral and Residues"

Lecture Notes: "Proof of Functional Equation of Riemann Zeta Function by Mellin Transform, Poisson Summation, and Gauss Error Function"

Lecture Notes: "Dirichlet Series, Abscissas of Convergence, and Growth Rate Along Vertical Lines"

Lecture Notes: "Gamma Function, Infinite Product Representation, Relation with Sine Function, Duplication Formula, and Stirling's Formula"

Lecture Notes: "Growth Rate of Riemann Zeta Function on Vertical Lines"

Lecture Notes: "Mean-Value and Oscillation Theorems"

Lecture Notes: "Theorem of Hardy-Littlewood on an Infinite Number of Zeroes of the Riemann Zeta Function on the Critical Line"

Lecture Notes: "Theorem of Borel-Caratheodory"

Lecture Notes: "Perron Formula Without Error Estimates"

Lecture Notes: "Explicit Formula for Logarithmic Derivative of Riemann Zeta Function"

Lecture Notes: "Width of Strip of all Zeta Function Zeroes and Error Term of Growth of Partial Sum of Dirichlet Series of Logarithmic Derivative of Zeta Function at the Origin"

Lecture Notes: "Prime Number Theorem"

Lecture Notes: "Lindelöf's Hypothesis"

Lecture Notes: "Theta Divisor"

Lecture Notes: "Theta Functions in Higher Dimension"