Introduction to Analytic Number Theory and Algebraic Number Fields

Code: MA721 | L-T-P-C: 4-0-0-8

MA721 Introduction to Analytic Number Theory and Algebraic Number Fields [4-0-0-8] Prerequisites: MA521 Modern Algebra

Arithmetic functions, Elementary theorems on distribution of prime numbers, Dirichlet's Theorem on primes in arithmetic progressions, Dirichlet series and Euler products, Zeta functions, Prime number theorem.

Number fields and Number rings, Prime decomposition in number rings, The ideal class group and the unit group, Dedekind zeta function and the class number formula, The distribution of primes and class field theory.

Texts:

1. Apostol, T.M., Introduction to Analytic Number Theory, UTM, Springer, 1976.
2. Marcus, D. A., Number Fields, Springer Verlag, 1977.
3. Janusz G.J. , Algebraic Number Fields, GSM, Vol-7 (2nd Ed.) AMS, 1996.