MA 317: Introduction to Analytic Number Theory

Credits: 3:0

Pre-requisites :

  1. MA 224 (complex Analysis) or equivalent
  2. An introductory course in Number Theory, or Consent of instructor

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, the Riemann zeta function and related objects, the prime number theorem. (Time permitting: advanced topics like sieves, bounds on exponential sums, zeros of functions. the circle method.)

Suggested books and references:

  1. Apostol, T.M., Introduction to Analytic Number Theory, Springer-Verlag, 1976.
  2. Davenport, H., Multiplicative Number theory, 3rd edition, Springer, 2000.

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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: 17 May 2024