Analytic Number Theory (2019)

  Convener(s)
Name: Prof. Anirban Mukhopadhyay Dr. G. Kasi Viswanadham Dr. Prem Prakash Pandey
Mailing Address: Associate Professor,
Institute of Mathematical Sciences,
4th Cross Road, CIT Campus,
Taramani, Chennai-600113.		 Assistant Professor,
IISER Berhampur,
Engg. School Road, NH-59, Berhampur,
Ganjam District, Odisha-760010.		 Assistant Professor,
IISER Berhampur,
Engg. School Road, NH-59, Berhampur,
Ganjam District, Odisha-760010.
Email: anirban at imsc.res.in viswanadh at iiserbpr.ac.in premp at iiserbpr.ac.in

Please Note:  Participants have to arrange for their own travel.

The prime number theorem and Dirichlet theorem on arithmetic progressions are two of the most classical and important results in analytic number theory. Their proofs show the interplay between the sums of arithmetical functions and certain complex valued functions. The aim of the first week is to present the proofs of these theorems.
In the second week of the school, we introduce the audience to sieve methods and show that how these methods can be applied to count certain interesting objects. We take utmost care to see that all the lectures are self contained; very minimal knowledge of number theory will be needed.

Dates: 

Monday, December 2, 2019 - 09:30 to Saturday, December 14, 2019 - 18:45

Venue: 

Venue Address: 

IISER Berhampur,
Engg. School Road, NH-59, Berhampur,
Ganjam District, Odisha-760010.

Venue State: 

Venue City: 

PIN: 

760010

Chrono Order: 

343

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

Selected Applicants: 

Instructions: We request the selected applicants to send their conformation to viswanadh@iiserbpr.ac.in by 31st August, 2019. The selected applicants should send a copy of their ticket, for their journey to Berhampur, to viswanadh@iiserbpr.ac.in at the earliest for conformation.

S.No. SID Full Name Gender University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A
1 28620 Mr Vishalkumar Jayantibhai Prajapati Male Municipal Arts and Urban Bank Science College Mehasana 2018
2 28621 Mr. Manoj Kumar Male University of Lethbridge 2013
3 28649 Dr Thiyam Rojita Chanu Male Manipur University 2008
4 28651 Mr. Snehashis Mukherjee Male University of calcutta 2018
5 28653 Dr. Fahed Zulfeqarr Male - 2002
6 28660 Mr. Sunil Kumar Sahoo Male Alagappa University 2007
7 28713 Ms. Pooja Sharma Female Banaras Hindu university Appeared
8 28715 Mr. Sandeep E M Male IISER Thiruvananthapuram 2015
9 28795 Mr Vatsal Pramod Jha Male IIT(ISM) Dhanbad Appeared
10 28998 Dr Kiran Virivinti Male Osmania University 2002
11 29034 Dr. Debashish Bose Male IIT Kanpur 2001
12 29036 Dr. Bandhu Prasad Male I. I. T Roorkee, Roorkee 2003
13 29065 Mr. Kalika Prasad Male Central University of Rajasthan 2017
14 29066 Ms. Munesh Kumari Female Central University of Rajasthan 2017
15 29068 Mr. Indrajeet Hazra Male Ballygnge Science College 2018
16 29076 Mr. Rahul Arora Male S.C.D Gov College 2008
17 29091 Dr. Priya Gupta Female VBS Purvanchal University, Jaunpur 2007
18 29092 Dr. Bibekananda Maji Male IIT Bombay 2010
19 29124 Mr. Mithun Kumar Das Male IIT Kharagpur 2012
20 29132 Mr Nabin Kumar Meher Male IIT kanpur 2011
21 29146 Ms Pratiksha Satish Shingavekar Female University of Pune 2017
22 29154 Dr. Anuj Jakhar Male IISER Mohali 2014
23 29156 Mr. C G Karthick Babu Male Madurai Kamaraj University 2014
24 29159 Ms. Aditiben Dineshbhai Savalia Female Sardar Patel University 2018
25 29160 Ms. Shashi Chourasiya Female IIT Gandhinagar -
26 29169 Mr. Shivajee . Male Not given 2017
27 29184 Dr. Shivaraj Kumar Male Mysore University/ M.Sc. 2006
28 29186 Dr. Neeraj Neeraj Male IISER mohali 2014
29 29196 Mr. J . Devendra Male Sri Venkateshwra University 2015
30 29199 Dr. Ashok Kumar Male University of Jammu 2001
31 29203 Mr. Aditya Bhan Ojha Male MDS university of Ajjmer 2009
32 29209 Ms Sagarika Dash Female Utkal University Appeared
33 29211 Ms. Pyari Punyatoya Harichandan Female Utkal University  
34 29219 Mr. Soumyaranjan Satapathy Male Utkal University  
35 29223 Mr Gorekh Prasad Sena Male University of Hyderabad 2015
36 29224 Ms Subhashree Tripathy Female - -
37 29234 Mr. Susobhan Mazumdar Male IIT Madras M.Sc 2010

 

Local Participants

S. No. SID Name Gender University/Institute Year of Passing M.Sc./M.A.
1 28741 Mr. Mahesh Kumar Ram Male IISER Berhampur -
2 28748 Mr. Sougata Pal Male IISER Berhampur -
3 28779 Mr. Arnab Roy Male IISER Berhampur -
4 28812 Mr. Pratik Sinha Male IISER Berhampur -
5 29069 Mr.Nimish Kumar Male IISER Berhampur -
6 29072 Mr. Priyaranjan Mallick Male IISER Berhampur -
7 29121 Mr. Dilip Kumar Sahoo Male IISER Berhampur -
8 29070 Dr. Anup Kumar Singh Male IISER Berhampur 2012

How to Reach: 

Click here

School Short Name: 

ant

Last Date Application: 

Monday, July 15, 2019

School Type: 

IST