Lectures on The Riemann Zeta-Function
by K. Chandrasekharan
Publisher: Tata Institute of Fundamental Research 1953
Number of pages: 154
The aim of these lectures is to provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here. The exposition is self-contained, and required a preliminary knowledge of only the elements of function theory.
Download or read it online for free here:
by Jan Nekovar - Institut de Mathematiques de Jussieu
Contents: Introduction; Abel's Method; A Crash Course on Riemann Surfaces; Cubic curves; Elliptic functions; Theta functions; Construction of elliptic functions; Lemniscatology or Complex Multiplication by Z[i]; Group law on smooth cubic curves.
by M. Beck, G. Marchesi, D. Pixton - San Francisco State University
These are the lecture notes of a one-semester undergraduate course: complex numbers, differentiation, functions, integration, Cauchy's theorem, harmonic functions, power series, Taylor and Laurent series, isolated singularities, etc.
by E. G. Phillips - Oliver And Boyd
This book is concerned essentially with the application of the methods of the differential and integral calculus to complex numbers. Limitations of space made it necessary for me to confine myself to the more essential aspects of the theory ...
by C.L. Siegel - Tata Institute of Fundamental Research
A systematic study of Riemann matrices which arise in a natural way from the theory of abelian functions. Contents: Abelian Functions; Commutator-algebra of a R-matrix; Division algebras over Q with a positive involution; Cyclic algebras; etc.