Tata Institute Of Fundamental Research Lectures On Mathematics

I want the lecture on “On the Riemann Zeta-Function” of Mathematics of Tata Institute Of Fundamental Research?

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Ok, here I am providing you the lecture on “On the Riemann Zeta-Function” of Mathematics of Tata Institute Of Fundamental Research by K. Chandrasekharan

TISS On the Riemann Zeta-Function Lecture

The aim of these lectures is to provide an introduction
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 on the
Zeros of (s), 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

Contents
1 The Maximum Principle
2 The Phragmen-Lindelof principle
3 Schwarz’s Lemma
4 Entire Functions
5 Entire Functions (Contd.)
6 The Gamma Function
1 Elementary Properties
2 Analytic continuation of _(z)
3 The Product Formula
7 The Gamma Function: Contd 55
4 The Bohr-Mollerup-Artin Theorem
5 Gauss’s Multiplication Formula
6 Stirling’s Formula
8 The Zeta Function of Riemann 63
1 Elementary Properties of _(s)
9 The Zeta Function of Riemann (Contd.)
2 Elementary theory of Dirichlet Series .




For complete lecture here is the attachment


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