Department of Mathematics

Indian Institute of Technology Bombay

Popular Lecture Series in Mathematics

Mathematics Association of IIT Bombay and Bombay Mathematical Colloquium

Speaker: Prof.Dipendra Prasad
Title: Algebraic Number Theory
Date: Friday 21 March, 2003
Time: 5.05 p.m.- 6.10 p.m.
Venue: Ramanujan Hall

The lecture will give an introduction to some aspects of algebraic number theory via concrete simple examples. The basicquestion used to illustrate the theory will be: how does a polynomialwith integral coefficients factorise modulo prime numbers. We will give an introduction to the Artin's primitive root conjecture, and discuss a question of Erd\os (answered by Corrales-Rodrigaqez and Schoof): if two integers m and n have the same order modulo p, for almost all primes p, then is m = n? Time permitting, we will discuss some generalisations which are an active area of research.