# Algebraic Number Theory: Home

Algebraic number theory is a major branch of number theory that studies algebraic structures related to algebraic integers.

## Welcome to the Algebraic Number Theory Course Guide! The resources within this guide have been specifically chosen for their usefulness to those studying Algebraic Number Theory. You can find useful databases, books, websites and more by using the tabs above.

## Using this Guide to Help with your Research

These Research Guides are designed by librarians to assist students studying at the Riphah International University. Use the tabs along the top edge of this box to locate various resources. You can use this research guide to help you with class assignments. The 'Getting Started' tab gives an overview of the steps you can take when researching an assignment in the Riphah International University Library. The following tabs cover the resources in more detail. If you run into obstacles, please don't hesitate to contact the Information Advisor.

## Course Description

A number field K is a finite algebraic extension of the rational numbers Q. Every such extension can be represented as all polynomials in an algebraic number ®: K = Q(®) = (Xm n=0 an®n:an2Q) . Here ® is a root of a polynomial with coefficients in Q. Algebraic number theory involves using techniques from (mostly commutative) algebra and finite group theory to gain a deeper understanding of number fields. The main objects that we study in algebraic number theory are number fields, rings of integers of number fields, unit groups, ideal class groups,norms, traces, discriminants, prime ideals, Hilbert and other class fields and associated reciprocity laws, zeta and L-functions, and algorithms for computing each of the above.