Recently analytic number theory has seen great progress. Zhang’s remarkable result on gaps between primes is a huge leap towards proving the twin prime conjecture. Zhang’s work has brought back to the forefront of research classical topics like exponential sums, sieve methods and large sieve.Moreover a proper perspective of the modern number theory can only be achieved based on a thorough knowledge of modular forms, automorphic forms and their L-functions.
The workshop will focus on these important branches in modern analytic number theory. The basic topics that will be covered include exponential sums, circle method, sieve methods, large sieve, modular forms, automorphic forms and L-functions. The participants are expected to have a sound knowledge in basic analysis (real and complex) and basic algebra. Some previous knowledge in elementary number theory will be very helpful. The lectures will start at a basic level, but are expected to conclude at a suitable high level
Time-table
9:45-11:15 | 11:30-1:00 | 2:15-3:45 | 4:15-5:45 | ||||
26 Dec | SD | T | RR | L | SR | T | Tutorial (SD) |
27 Dec | RR | E | SD | U | SB | E | SR |
28 Dec | SR | A | SD | N | SB | A | Tutorial (SR) |
29 Dec | RR | SD | C | SB | Tutorial (RR) | ||
30 Dec | RR | SB | H | SR | Tutorial (SB) |
Speakers:
1) Soumya Das (SD): Classical modular forms
2) Ravi Raghunathan (RR): Automorphic forms and L-functions
3) Surya Ramana (SR): Sieve methods and large sieve
4) Stephan Baier (SB): Exponential sums and circle method
References:
- Iwaniec and Kowalski – Analytic Number Theory
- Montgomery – Ten Lectures on the Interface of Analytic Number Theory and Harmonic Analysis
- Miyake – Modular Forms
- Gelbart – Automorphic Forms on Adele Groups
- Friedlander and Iwaniec - Opera de Cribro
Names of the tutors
- Arpit Bansal
- Pramath Anamby
- Pramod Kewat
- Mallesham Kummari