Integrated MSc-PhD Program

SYLLABUS

KSM3E07: Number Theory

The Fundamental Theorem of Arithmetic, Arithmetic  Functions and Dirichlet Multiplication, Mean Values of Arithmetic Functions,  Characters and Dirichlet Characters, Gauss Sums, Primitive Roots  and Quadratic Residues, Primes in Arithmetic Progression, Dirichlet Series and Euler Products, The Riemann Zeta Function  ,  Prime Number Theorem,  L-functions, Revisiting the Prime Number Theorem.

Suggested texts:

1. 1. 1. 1. 1. 1. T.M. Apostol, Introduction to Analytic Number Theory, Undergraduate texts in Mathematics, Springer-Verlag, 1976.
               2. R. Ayoub, An Introduction to the Analytic Theory of Numbers, American Mathematical Society (AMS), 1963.
               3. H. Davenport, Multiplicative Number Theory, Graduate Texts in Mathematics (GTM), Springer-Verlag GTM, 2000.
               4. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers (with an appendix by Andrew Wiles and Roger Heath-Brown), Oxford University Press, 2008.