IST - Analytic Number Theory (2019)

Speakers and Syllabus


Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
Prof. Satadal Ganguly, ISI Kolkata, Kolkata 6 Properties of the Riemann zeta function: Analytic continuation, Functional equation, Bounds in the critical strip. Perron’s formula, Proof of the prime number theorem
Prof. Anirban Mukhopadhyay, Institute of Mathematical Sciences, Chennai 6 Sieve of Eratosthenes, Selberg Sieve, Applications to twin prime and Goldbach conjecture
Dr. Prem Prakash Pandey, Indian Institute of Science Education and Research Berhampur 6 A survey of prime generating functions, infinitude of prime values of irreducible polynomials with no fixed divisor (Buniyakowsky's conjecture), Known results on Buniyakowsky's conjecture. Square- free values of polynomials: proof for quadratic polynomials (using sieve of Eratosthenes), and the general conjecture.
Dr. G. Kasi Viswanadham, Indian Institute of Science Education and Research Berhampur 6 Infinitude of primes (Euler’s proof), Primes of the form 4n+1, Dirichlet characters and their properties, Dirichlet theorem on arithmetic progressions

 References:
1. G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory
2. Halberstam and Richert, Sieve Methods
3. Lecture notes from speakers

Tutorial Assistants:

S. No. Name Affiliation
1 Dr. K. Mallesham ISI, Kolkata

 

 


Time Table

Day Date Lecture 1
(9.30–11.00)
Tea
(11.05 – 11.25)
Lecture 2
(11.30–1.00)
Lunch
(1.05– 2.25)
Tutorial
(2.30– 3.30)
Tea
(3.35- 3.55)
Tutorial
(4.00- 5.00)
Snacks
5.05- 5.30
Mon 02-12- 2019 PPP   GKV   PPP+T   GKV+T  
Tues 03-12- 2019 PPP   GKV   PPP+T   GKV+T  
Wed 04-12- 2019 PPP   GKV   PPP+T   GKV+T  
Thu 05-12- 2019 PPP   GKV   PPP+T   GKV+T  
Fri 06-12- 2019 PPP   GKV   PPP+T   GKV+T  
Sat 07-12- 2019 PPP   GKV   PPP+T   GKV+T  
SUNDAY : 08-12-2019
Mon 09-12- 2019 AM   SG   AM+T   SG+T  
Tues 10-12- 2019 AM   SG   AM+T   SG+T  
Wed 11-12- 2019 AM   SG   AM+T   SG+T  
Thu 12-12- 2019 AM   SG   AM+T   SG+T  
Fri 13-12- 2019  AM   SG   AM+T    SG+T   
Sat 14-12- 2019 AM   SG   AM+T   SG+T  

Abbreviations used:
SG- Prof. Satadal Ganguly,ISI Kolkata
GKV- Dr. G. Kasi Viswanadham, IISER Berhampur
AM- Prof. Anirban Mukhopadhyay, IMSc, Chennai
PPP- Dr. Prem Prakash Pandey, IISER Berhampur

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