Number Theory
Number Theory
Number Theory
The candidate will be expected to have a command of two of the three branches of number
theory (elementary, algebraic and analytic) and have an acquaintance with the basic concepts,
techniques and major theorems of the third.
2. Congruences
3. Primitive roots
4. Quadratic reciprocity
5. Gauss sums
(a) Poisson summation, analytic continuation, and the functional equation for the zeta
function
(b) Zeros of the zeta function, trivial, non-trivial, Riemann Hypothesis
Local Theory:
1. Valuations
2
References:
Elementary Number Theory
1. Adams, Goldstein: Introduction to Number Theory