IST - Analytic Number Theory (2019)

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

Tea

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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