Number Theory What Are Some Recommended Books for Learning p-adic Numbers?

[bacte2013]

Dear Physics Forum friends,

what are some good books for learning the p-adic numbers? What are the necessary pre-requisites?
Do I need to know introductory number theory or basics of algebraic/analytic number theory?

 

[The Bill]

I don't have experience per-se, but I have been thinking of learning the same things, and did a tiny bit of research on books for this a couple months ago.

The most recommended book was "p-adic Numbers: An Introduction" by Fernando Gouvea. In the introduction, Gouvea states that "the pre-requisites for reading this book are a basic knowledge of algebra and number theory, and a few courses in calculus or analysis." He says the reader needs to know congruences, fields and rings, and the basic facts of point-set topology, continuity, and infinite series. From context, he probably means you need to know the basic topology and properties of continuity and infinite series one learns in an undergraduate analysis course.

 

[Ssnow]

''p-adic numbers, an introduction'', Gouvea Fernando , Springer