Find a Book About Prime Number Distribution

[Treadstone 71]

I'm looking for a book that will do a thorough exposition of everything we know about the distribution of primes. Can anyone recommend one?

 

[rhj23]

'The Distribution Of Prime Numbers' - A.E.Ingham is pretty good, but then it's the only one I've used so there may be better suggestions out there..

 

[shmoe]

I don't think there is a book that contains "everything".

Ingham's book is old, but also one of my favorites, it's a great introduction though at an advanced level. "The Prime Numbers and their distribution" by Tenenbaum, et al. is a nice book as well, more on an introductory level but still covering a good range of topics.

Almost all number theory texts beyond the "elementary" ones will have info on the distribution of primes. Davenport's "Multiplicative Number theory" and Apostols "Introduction to Analytic Number Theory" are good. "Analytic Number Theory" by Iwaniec and Kowalski is a phenomenal resource for all things related to it's title, though perhaps not the easiest to learn about a topic from scratch.

Guy's "Unsolved Problems In Number Theory" is self explanatory. It usually gives the most current results on a topic and will provide ample references.

If you plan to buy a book, you should go to the library and try to read some of it first to see if it's at an appropriate level.

 

[Treadstone 71]

Thanks for the suggestions. I've discovered a book called "Prime Numbers: The Most Mysterious Figures in Math" which I really like. It may sound like a popularized math book, but it's actually like "Unsolved Problems in Number Theory" by Guy, though it lists topics that are solved and unsolved. "The New Book of Prime Number Records" is pretty good too.

Guy's book is very discouraging to read. At the end of many sections, he often includes a remark like "it is unlikely that this problem will be solved within our lifetime".

 

[shmoe]

In number theory, hundreds and thousands of pages of work can result in reducing an exponent by a minuscule amount and still you seem hopelessly distant from what is believed to be the truth.