**Complex Analysis on Riemann Surfaces**

by Curtis McMullen

**Publisher**: Harvard University 2005**Number of pages**: 89

**Description**:

Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; Line bundles; Curves and their Jacobians; Hyperbolic geometry; Quasiconformal geometry.

Download or read it online for free here:

**Download link**

(560KB, PDF)

## Similar books

**On Riemann's Theory of Algebraic Functions and their Integrals**

by

**Felix Klein**-

**Macmillan and Bowes**

In his scholarly supplement to Riemann's complex mathematical theory, rather than offer proofs in support of the theorem, Klein chose to offer this exposition and annotation, first published in 1893, in an effort to broaden and deepen understanding.

(

**7125**views)

**Lectures On The General Theory Of Integral Functions**

by

**Georges Valiron**-

**Chelsea Pub. Co.**

These lectures give us, in the form of a number of elegant and illuminating theorems, the latest word of mathematical science on the subject of Integral Functions. They descend to details, they take us into the workshop of the working mathematician.

(

**1085**views)

**Complex Analysis**

by

**Christian Berg**-

**Kobenhavns Universitet**

Contents: Holomorphic functions; Contour integrals and primitives; The theorems of Cauchy; Applications of Cauchy's integral formula; Zeros and isolated singularities; The calculus of residues; The maximum modulus principle; Moebius transformations.

(

**1368**views)

**Lectures on Modular Functions of One Complex Variable**

by

**H. Maass**-

**Tata institute of Fundamental Research**

This is an elementary introduction to the theory of modular functions and modular forms. Basic facts from the theory of functions of a complex variable and some properties of the elementary transcendental functions are the only prerequisites.

(

**4583**views)