- Thread starter
- #1

- Jan 17, 2013

- 1,667

What else should I read about to fully understand the zeta function and its zeros ?

- Thread starter ZaidAlyafey
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- Thread starter
- #1

- Jan 17, 2013

- 1,667

What else should I read about to fully understand the zeta function and its zeros ?

- Mar 22, 2013

- 573

You have to have a background in Complex Analysis to learn about zeta. I don't know how much have you learned so I can't tell whether you need to learn more or not. After CA, you must learn a little basics on ring theory and field theory since algebraic number theory should be learned when you are going towards zeta. Analytic number theory is the last and the most important tool for zeta.ZaidAlyafey said:What else should I read about to fully understand the zeta function and its zeros ?

In other words, you have to learn Number Theory in order to understand zeta.

Well, you can approach from other direction like Physics, Complex Dynamics, etc but that would take quite long for you since you are familiar with analytical methods the most.

Hope this helps,

Balarka

.

- Thread starter
- #3

- Jan 17, 2013

- 1,667

My knowledge in CA is basically the topics discussed in any standard CA book , I can't claim I am an expert in that but I found it interesting enough for my especially the residue theorem.

I started reading a book ( Introduction to the theory of Riemann zeta function) I can say I have now difficulty until now , in the general understanding.

Number theory is a very general subject , I can't just go and read every thing about it as I don't have time for that, what I am thinking about is reading the book and if anything I don't get I go and read about it .

- Mar 22, 2013

- 573

I don't know what do you mean by standard book, since I never learned anything in CA from a book. I have one, yes, but it is too restricted on Residues which isn't my area of working.My knowledge in CA is basically the topics discussed in any standard CA book , I can't claim I am an expert in that but I found it interesting enough for my especially the residue theorem.

Here is a list of CA topics and tell me which do you know about :

Riemann Surface, Mittang-Leffler's expansion, Weierstrass Factorization, Analytic functions, Casorati–Weierstrass theorem.

About the book you are reading, Introduction to the theory of Riemann zeta function, the name doesn't ring the bell, can you specify the writers?

Oh, so you want to read as much as you can comprehend, right? So try Titchimarsh & Health-Brown first.

- Thread starter
- #5

- Jan 17, 2013

- 1,667

For example , "First Course in Complex Analysis " By Zill.I don't know what do you mean by standard book,

You mean you depend on google search and papers?since I never learned anything in CA from a book. I have one, yes, but it is too restricted on Residues which isn't my area of working.

I only know about Riemann Surface and Analytic functions.Here is a list of CA topics and tell me which do you know about :

Riemann Surface, Mittang-Leffler's expansion, Weierstrass Factorization, Analytic functions, Casorati–Weierstrass theorem.

By Patterson.About the book you are reading, Introduction to the theory of Riemann zeta function, the name doesn't ring the bell, can you specify the writers?

I can't find this book online !.Oh, so you want to read as much as you can comprehend, right? So try Titchimarsh & Health-Brown first.

- Mar 22, 2013

- 573

You know about Riemann Surfaces? Wow, that's good! Do you know about elliptic curves?

Oh, yes, finding it in the internet is a pain. I guess you have to go with Patterson then. Can you specify the parts you don't understand? Maybe we can help then.

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- #7

- Jan 17, 2013

- 1,667

No , just heard about it , I cannot read about everything I hear about , this will not end .You know about Riemann Surfaces? Wow, that's good! Do you know about elliptic curves?

Sure , I will post any thing I don't understand.Oh, yes, finding it in the internet is a pain. I guess you have to go with Patterson then. Can you specify the parts you don't understand? Maybe we can help then.