AIS Analytic Number Theory (2015) - Speakers and Syllabus

There have been spectacular developments in Analytic Number Theory in recent  times. The main theme of this school is to introduce emerging themes and progress in Analytic Number Theory. Starting from basic concepts the school aims to cover : Equidistribution and Modular Forms; Maass Forms and Galois Representations; Applications of linear forms in logarithms; Recent developments in sieve theory; Zeta and L-functions. Some open problems will also be presented.

Proposed Syllabus

Speakers Duration Details of the syllabus
K. Srinivas 9 Introduction to Basic Techniques in Analytic Number Theory : Arithmetical functions, asymptotic estimates,
analytical  properties of the Riemann zeta-function, prime number theorem.
R. Thangadurai 9 Introduction to Basics of Modular Forms : Modular group, action on upper half plane, fundamental domains; Modular forms of
weight k, dimension formula; Hecke operators and their multiplicative property; Eigen functions of Hecke operators;
Estimates of Fourier coefficients of Modular forms.
Ritabrata Munshi 4.5 Convexity and sub-convexity results of Zeta and L-functions and their applications.
Kaneenika Sinha 4.5 Equidistribution problems in modular forms: Explicit estimation of the characteristic function of an interval by trigonometric polynomials and their
application to the study of equidistribution of Fourier coefficients of modular forms.
Shanta Laishram 4.5 Linear forms in logarithms and applications: Introduction of Baker’s theory of linear forms in logarithms, application to some diophantine equations
and approximations.
Michel Waldschmidt 4.5 Transcendental numbers: Introduction to some of the main methods and to some of the open problems.
Ram Murty 9 Recent developments and some open problems in analytic number theory.
Kumar Murty 9 Modular forms, Artin L-functions, Maass forms and Galois representations, recent  progress and some open problems.

Time Table

    Lecture 1 Tea Lecture 1 Lunch Tutorial Tea
  Dates 9:30-11:00   11:30-1:00 1:00-2:00 2:00-4:00 4:00-4:15
Week1 1/6/2015 KS TD      
  2/6/2015 KS TD
  3/6/2015 KS TD
  4/6/2015 KS TD
  5/6/2015 KS TD
  6/6/2015 KS TD
week2 8/6/2015 SK SL
  9/6/2015 SK SL
  10/6/2015 SK SL
  11/6/2015 RM RI
  12/6/2015 RM RI
  13/06/2015 RM RI
week3 15/06/2015 RM KM
  16/06/2015 RM KM
  17/06/2015 RM KM
  18/06/2015 MW KM
  19/06/2015 MW KM
  20/06/2015 MW KM


Name of Speakers Affiliation
K. Srinivas (KS) IMSc, Chennai
Kaneenika Sinha (SK) IISER, Pune
Ram Murty(RM) Queens Univ, Kingston, Canada
R. Thangadurai (TD) HRI, Allahabad
Shanta Laishram (SL) ISI, Delhi
Ritabrata Munshi (RI) TIFR, Mumbai
Michel Waldschmidt (MW) Université Pierre et Marie Curie (Paris 6) , France
Kumar Murty (KM) University of Toronto, Canada
Course associates
Name of Speakers Affiliation
Brundaban Sahoo NISER Bhubaneswa
Jaban Meher IISc, Bangalore
Kamalakshya Mahatab IMSc, Chennai
Usha Sangale SRTM, Nanded
Sudheer Pujahari IISER, Pune
Subramani Muttukrishnan CMI, Chennai