AIS Analytic Theory of Algebraic Numbers (2016)- Speakers and Syllabus

The event is Cosponsored by The Institute of Mathematical Sciences, Chennai

A brief description :-

The school aims to equip researchers in number theory and university lecturers who teach number theory with fundamental concepts, problem solving techniques in algebraic and analytic number theory and update them with recent developments in the subject.

Proposed Syllabus

Speaker hrs Details of the syllabus
K. Srinivas 9 Introduction to analytic number theory : basic tools, Riemann zeta- function, proof of prime number theorem. L- functions associated to various objects.
Kaneenika Sinha 9 Euclidean rings, algebraic numbers and integers, integral bases, Dedekind domains.
Ritabrata Munshi 9 A brief survey of recent developments in analytic number theory and some open problems.
R. Thangadurai 9 The Ideal class group, Gauss sums, quadratic fields, Dirichlet’s unit theorem, units in real quadratic fields
Stephan Baier 9 The theory of exponential sums: the methods of Weyl, van der Corput, A and B processes, applications to divisor problem, Gauss circle problem, bounds of Riemann zeta function in the critical strip.
Kumar Murty 9 Higher reciprocity laws and introduction to class field theory.

 Reference books:

  1. Problems in Algebraic Number Theory : Esmonde and Ram Murty
  2. Algebraic Number Theory : H. Pollard
  3. Algebraic Number Theory : Marcus
  4. Introduction to Analytic Number Theory : Apostol
  5. The theory of Riemann zeta function : E. C. Titchmarsh
  6. Lattice points : Kratzel
    Lecture 1 Tea Lecture 2 Lunch Tutorial Tea
  Day 9.30-11.0 0                     11.30-1.0 0                     2.00-4.00 4.00-4.15
Week 1 1 SK KS                                     
      2 SK KS
3 SK KS
4 SK KS
5 SK KS
6 SK KS
Week 2 1 TD RM
      2 TD RM
3 TD RM
4 TD RM
5 TD RM
6 TD RM
Week 3 1 KM SB
      2 KM SB
3 KM SB
4 KM SB
5 KM SB
6 KM SB Bye

 Speakers

K. Srinivas (SK) IMSc, Chennai Kaneenika Sinha (KS) IISER, Pune R. Thangadurai, HRI, Allahabad
Ritabrata Munshi (RI) TIFR, Mumbai & ISI, Kolkata Kumar Murty (KM) University of Toronto,Canada Stephan Baier, IISER, Trivandrum

 Tutors :

  1. Kashi Viswanath (IMSc, Chennai),
  2. Kamalakshya Mahatab (IMSc, Chennai),
  3. Senthil Kumar (IMSc, Chennai),
  4. Usha Sangale (SRTM Univ, Nanded),
  5. Jaban Meher (IISc, Bangalore),
  6. Brundavan Sahoo (NISER, Bhubaneswar).