IST - Analytic Number Theory (2019)

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Venue:

IISER,  Berhampur, Odisha(Orissa)

Date: 

2nd, Dec 2019 to 14th, Dec 2019

 

School 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.

 


Names of the tutors and their affiliation :

   
    (1) Dr. Anup Kumar Singh, IISER Berhampur
    (2) Dr. Kummari Mallesham, ISI Kolkata
    (3) Mr. Mithun Das, HRI Allahabad
    (4) Mr. Prahlad Sharma, ISI Kolkata
    (5) Gopal Maity, ISI Kolkata

 


 Syllabus: 

Sl. No.

Speaker

Syllabus covered by each speaker

1

Dr. Prem Prakash Pandey,
IISER Berhampur

These lectures started with a  survey of prime generating functions, for example the result of Mills and Wilson’s formula etc. The speaker introduced the conjecture asserting  infinitude of prime values of irreducible polynomials with no fixed divisor (Buniyakowsky's conjecture),  and stated  the current status of the Buniyakowsky's conjecture. Then the speaker spoke on square-free values of polynomials. He has given proof for the infinitude of square-free values of quadratic polynomials (using sieve of Eratosthenes), and he has concluded the lecture series with the general conjecture. In the tutorials sessions the exercises given in the lecture were solved/discussed.

2

Dr. G. Kasi Viswanadham,
IISER Berhampur

The speaker started with Euclid’s proof of infinitude of primes; infinitude of primes of the form 3n+2,  4n+3 and 4n+1. Then the Euler’s proof of infinitude of primes ( sum of reciprocal of primes diverges) was given. Then he has introduced the conjecture of Euler and Legendre on the infinitude of primes in arithmetic progressions and mentioned the result of Ram Murty which says that the Euclid’s proof can not be given for infinitude of primes in AP. The speaker then introduced Dirichlet series, Dirichlet Characters, Dirichlet L-functions. In the fifth lecture it was shown that the sum over a(mod q) of \frac{\Lambda(n)}{n} is given assuming Landau’s theorem on Dirichlet series with non-negative coefficients. The lecture is devoted to give a proof of  Landau theorem and to discuss further questions on primes in arithmetic progressions.

3 Dr. Anirban Mukhopadhyay, IMSc Chennai

These lectures started with an introduction to Sieve of Eratosthenes, after that the speaker proved the main  theorem of Selberg sieve, and its applications to counting primes and twin primes. The speaker spent his last two lectures on the Brun Sieve.

4 Dr. Satadal Ganguly, ISI Kolkata

These lectures aimed at proving the Prime number theorem. The speaker introduced the Riemann zeta function for Re(s)>1 and showed the analytic continuation using the theta series. Later he proved the zero free region of this function and some other results on the zeros of Riemann zeta function were obtained. Finally he has proved the Perron’s formula and as an application prime number theorem was obtained. The Lectures ended with the improvement of error term in prime number theorem under Riemann hypothesis.

 

 


 Time Table

 

 

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.05
to
11.25)

Lecture 2

(11.30
to
1.00)

Lunch

(1.05
to
2.25)

Tutorial

(2.30
to
3.30)

Tea

(3.35
to

3.55)

Tutorial

(4.00-5.00)

Snacks

(5.05
to
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

 

 

Saturday: 14-12-2019

 

Lecture-1

9:30
to
11:00

11:05
to
11:25

Lecture-2

11:30
to
1:00

 

1:00
to
2:00

2:00
to
3:00

3:00
to
3:15

3:15
to
4:15

4:15
to
4:30

4:30
to
5:30

5:30
to
6:00

AM

Tea

SG

Lunch

Tutorial

 

Teal

Tutorial

 

High Tea

Unity of Math Lecture

Valedictory

 * Unity of Mathematics lecture is given by Prof. Michel Waldschmidt.

 


List of actual Participants

 

S.No. SID Full Name Gender University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A
 1 29070 Dr. Anup Kumar Singh Male IISER Berhampur 2012
 2 28741 Mr. Mahesh Kumar Ram Male IISER Berhampur  
 3   Pramod patil Male Shivaji University, Kholapu  
 4 28779 Mr. Arnab Roy Male IISER Berhampu  
 5 29069 Mr.Nimish Kumar Male IISER Berhampu  
 6 29121 Mr. Dilip Kumar Sahoo   IISER Berhampur  
 7   Sourav Kanthi Patra   IISER Berhampur  
 8 29072 Mr. Priyaranjan Mallick Male IISER Berhampur  
9 28651 Mr. Snehashis Mukherjee Male University of calcutta 2018
10 28653 Dr. Fahed Zulfeqarr Male - 2002
11 28715 Mr. Sandeep E M Male IISER Thiruvananthapuram 2015
12 28795 Mr Vatsal Pramod Jha Male IIT(ISM) Dhanbad Appeared
13 28998 Dr Kiran Virivinti Male Osmania University 2002
14 29065 Mr. Kalika Prasad Male Central University of Rajasthan 2017
15 29066 Ms. Munesh Kumari Female Central University of Rajasthan 2017
16 29068 Mr. Indrajeet Hazra Male Ballygnge Science College 2018
17 29092 Dr. Bibekananda Maji Male IIT Bombay 2010
18 29132 Mr Nabin Kumar Meher Male IIT kanpur 2011
19 29156 Mr. C G Karthick Babu Male Madurai Kamaraj University 2014
20 29159 Ms. Aditiben Dineshbhai Savalia Female Sardar Patel University 2018
21 29160 Ms. Shashi Chourasiya Female IIT Gandhinagar -
22 29169 Mr. Shivajee . Male Not given 2017
23 29184 Dr. Shivaraj Kumar Male Mysore University/ M.Sc. 2006
24 29199 Dr. Ashok Kumar Male University of Jammu 2001
 25 28812 Mr. Pratik Sinha Male IISER Berhampur  
 26 28748 Mr. Sougata Pal Male IISER Berhampur  
 27   George David Tigga Male IISER Berhampur  

 


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