IST Number Theory (2015)- Speakers and Syllabus

Syllabus:

Name of the Speaker with Affiliation Lectures Detailed Syllabus
A. Mukhopadyaya,IMSc, Chennai
(AM)
4 (6 hours)

Dirichlet Character and Dirichlet Prime NumberTheorem

S. A. Katre, University of Poona, Pune
(SA)
4 (6hours) Distribution of Prime Numbers which includes infinitude of prime numbers, Chebychev estimate, Betrands postulate, elementary prime
number theorem.
S. D. Adhikari,HRI, Allahabad
(SDA)
4 (6 hours) Congruences includes basic linear congruences, Chinese Reminder Theorem, quadratic congruences, quadratic reciprocity law, finding
square-root modulo prime and Lagrange Theorem for Polynomial congruences
M. Manickam, KSOM, Calicut
(MM)
4 (6 hours) Distribution of Prime Numbers which includes infinitude of prime numbers, Chebychev estimate, Betrands postulate, elementary prime
number theorem.Congruences includes basic linear congruences, Chinese Reminder Theorem, quadratic congruences, quadratic reciprocity law, finding square-root modulo prime and Lagrange Theorem for Polynomial congruences
R. Thangadurai,HRI,Allahabad
(RT)
4 (6 hours) Induction (weak, strong) equivalent to the well - ordering principle,Decimal expansion of real numbers in base b, Continued fractions of
real numbers.
B. Ramakrishnan,HRI, Allahabad
(BR)
4 (6 hours) Arithmetical functions, summatory functions, partial summation formula, its application to summatory functions and estimates.

*SDA and SA sharing topics with MM

References:

1.Introduction to Analytical Number Theory by Tom M Apostol

Time-Table (with initials of speakers and course associates for entire days of the programme ):

Day Date Lecture 1
(9.30–11.00)
Tea
(11.00–11.30)
Lecturer 2
(11.30–1.00)
Lunch
(1.00–2.30)
Tutorial 1
(2.30–3.30)
Tea
(3.30-4.00)
Tutorial 2
(4.00-5.00)
Snacks
5.00-5.30
Mon 05-10-2015 RT   BR   Tut   Tut  
Tue 06-10-2015 RT   BR   Tut   Tut  
Wed 07-10-2015 RT   BR   Tut   Tut  
Thu 08-10-2015 RT   BR   Tut   Tut  
Fri 09-10-2015 SA   SDA   Tut   Tut  
Sat 10-10-2015 SA   SDA   Tut   Tut  
Sunday
Mon 12-10-2015 SA   SDA   Tut   Tut  
Tue 13-10-2015 SA   SDA   Tut   Tut  
Wed 14-10-2015 AM   MM   Tut   Tut  
Thu 15-10-2015 AM   MM   Tut   Tut  
Fri 16-10-2015 AM   MM   Tut   Tut  
Sat 17-10-2015 AM   MM   Tut   Tut