References for Number Theory, MSC 11

Elementary Number Theory, MSC 11A

1. G. H. Hardy, E. M. Wright, An Introduction To The Theory Of Numbers, Oxford University Press, London.

   An introductory book which is both comprehensive and comprehensible.

2. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998.

Sequences and sets, MSC 11B

1. Halberstam and Roth, Sequences, Oxford Clarendon Press

   This well-written book is somewhat outdated by now, but it is an excellent source to learn the basics from.

2. Nathanson, Inverse Problems and Geometry of Sumsets, Springer

   The inverse problem in additive number theory is the problem of inferring the structure of summands from the structure of the sumset. The book is the most complete source for information on such problems.

Diophantine equations, MSC 11D

1. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998.

Arithmetic algebraic geometry (Diophantine geometry), MSC 11G

1. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998.

Exponential sums and character sums, MSC 11L

1. E. C. Titchmarsh, The Theory of the Riemann Zeta-function. second ed. Oxford Science Pub. 1986

   The book covers the classical methods of Weyl, van der Corput/Phillips as well as mean-value method of Vinogradov.

Multiplicative number theory, MSC 11N

1. Davenport, Multiplicative number theory. Markham Publishing Comp., Chicago.

   Carefully written and motivated introduction to the multiplicative number theory.

Algebraic Number Theory: Global Fields, MSC 11R

1. Serge Lang, Algebraic Number Theory. Springer-Verlag, New York.
2. Daniel A. Marcus, Number Fields, Springer, New York.
3. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998.

Cyclotomic Extensions, MSC 11R18

1. Lawrence C. Washington, Introduction to Cyclotomic Fields, Springer-Verlag, New York.

Galois Cohomology, MSC 11R34

1. J. P. Serre, Galois Cohomology, Springer-Verlag, New York.

Algebraic Number Theory: Local Fields and $p$ adic Fields, MSC 11S

1. Serge Lang, Algebraic Number Theory. Springer-Verlag, New York.
2. Jean Pierre Serre, Local Fields, Springer-Verlag, New York.
3. Senon I. Borewicz, Igor R. Šafarevic, Zahlentheorie, Birkhäuser Verlag, Basel und Stuttgart (1966).

Finite fields and finite commutative rings (number-theoretic), MSC 11T

1. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998.