MA 352: Introduction to Analytic Number Theory

Credits: 3:0

Pre-requisites :

  1. Introductory courses in basic number theory
  2. Complex analysis

Review of arithmetical functions, Averages of arithmetical functions, Elementary results on the distribution of prime numbers, Dirichlet characters, Dirichlet’s theorem on primes in arithmetic functions, Dirichlet series and Euler products, Riemann zeta function and related objects, The prime number theorem.

(Time permitting: More advanced topics like Sieves, bounds on exponential sums, zeros of zeta functions, circle method etc.)

Suggested books and references:

  1. H. Davenport., Multiplicative Number Theory, Springer GTM 74 (third ed.) 2000.
  2. Tom. M. Apostol., Introduction to Analytic Number Theory, Springer-Verlag, 1976.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 14 Jul 2024