AIS Analytic Number Theory (2013)

Venue: KIIT, Bhubaneswar
Dates: 10th June to 30th June, 2013


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name K. Srinivas  Veena Goswami
Mailing Address Professor,
The Institute of Mathematical Sciences
C.I.T. Campus, Taramani, P.O.
Chennai - 600 113
KIIT School of Computer Applications ,
KIIT University, Bhubaneswar
751024, Odisha


Speakers and Syllabus 

A fundamental object of study in Analytic number theory is the distribution of primes. Many problems in mathematics require the techniques of analytic number theory.   Analytic number theory is extensively used in cryptography. The aim of this school is to equip researchers with the fundamental techniques and tools of analytic number theory, expose them to current developments in the subject and show them some future directions.

 Proposed Syllabus


Speaker Hrs Details of syllabus
T. N. Shorey 9 Introduction to Transcendental number theory:Irrationality , transcendence and algebraic independence of numbers connected with the exponential function at algebraic points and more generally of values of E-functions at algebraic values, Gelfond-Schneider and Baker theorem with applications.
Sinha Kaneenika 9 Arithmetical functions, averages of arithmetical functions, Euler's summation formula, Abel's summation formula, Chebyshev type estimates,  Dirichlet series, Riemann zeta-function, prime number theorem, Dirichlet theorem on primes in arithmetic progressions.
K. Srinivas 9 Zeros of the Riemann zeta-function, zero density estimates, difference between consecutive primes,  Riemann Hypothesis and its implications,  Bombieri-Vonogradov theorem.
R. Thangadurai 9 Sieve methods: Eratosthenes sieve, Sieve of Brun, Selberg Sieve, applications of sieve methods. Weyl's criteria for uniform distribution, Large sieve.
Ram Murty 9 Recent progress in analytic number theory and future directions: some open problems.
R. Padma 9 Introduction to algebraic number fields, finite fields, zeta functions associated to these fields, applications of analytic number theory to cryptography.




Lecture 1



Lecture 2







Week 1 1
SK   TNS      
  2 SK TNS
Week 2
  2 KS TD
4 RM
Week 3
  2 RM RP
4 KS
5 KS
6 KS RP Bye


T. N. Shorey (TNS)
IIT Mumbai
Sinha Kaneenika (SK)
K. Srinivas (KS)
IMSc Chennai
R. Thangadurai (TD)
HRI, Allahabad
Ram Murty (RM)
Queens Univ,Kingston, Canada
R. Padma,(RP)
VIT Vellore


Shanta Laishram Singh
     ISI, Delhi
Narasimha Kumar
IIT, Hyderabad
Bhavin Moria
IMSc, Chennai


Selected Applicants


Sr. SID Full Name Gender Affiliation State Position in College/ Univ. Univ./Inst. M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 2883 Mr Prasanta Kumar Sahoo Male Pondicherry Univ. Orissa M.SC Pondicherry Univ.  Appeared/ Awaiting Result  
2 2895 Dr Ashok Kumar Goli Male MVGRR Degree College Andhra Pradesh Reader In Mathematics Osmania Univ., Hyderabad 1985 4 May 1992
3 2913 Ms Saranya G Nair Female IIT Bombay Maharashtra PhD Cochin Univ. Of Science & Technology 2010  
4 2914 Mr Praveen Kumar Lavudi Male Andhra Univ. Andhra Pradesh Research Scholar Andhra Univ. 2008  
5 2942 Mr Sudhansu Sekhar Rout Male NIT Rourkela   Research Scholar Utkal Univ., Bhubaneswar. 2007  
6 2975 Mr. Bibekananda  Maji Male Harish-Chandra Research Institute Uttar Pradesh PhD Student IIT BOMBAY 2010  
7 2987 Ms. Debika  Banerjee Female Harish-Chandra Research Institute Uttar Pradesh PhD Scholar IIT Kanpur 2011  
8 3194 Mr Manjil P Saikia Male Tezpur Univ. Assam Integrated MSc Student Tezpur Univ. NA  
9 3337 Ms Akshaa  Vatwani Female Queen's Univ., Kingston, Ontario, Canada Ontario, Canada Graduate Student (PhD) IISER, Pune 2012  
10 3364 Mr. Raj Kumar Mistri Male IIT Patna Bihar Research Scholar  (JRF  Mathematics) TIFR Centre for Applicable Mathematics, Bangalore 2012  
11 3393 Mr Akhilesh  P Male Harish-Chandra Research Institute Uttar Pradesh PhD National Institute of Technology Calicut 2009  
12 3395 Mr. Rakesh Barai Ramlal Male Guru Nanak Khalsa College Maharashtra Asst. Prof. Univ.  of Mumbai 2001  
13 3411 Mr. Pallab Kanti Dey Male Harish-Chandra Research Institute Uttar Pradesh PhD Ramakrishna Mission Vidyamandira 2010  
14 3430 Mrs Usha Keshav Sangale Female SRTM Univ. Maharashtra Asst. Prof. Pune 2008  
15 3459 Mr Kamalakshya  Mahatab Male Institute of Mathematical Sciences Tamil Nadu PhD Institute of Mathematical Sciences, Chennai 2012  
16 3460 Mr. Sudhir Kumar Pujahari Male IISER – Pune Maharashtra PhD Utkal Univ. 2008  
17 3483 Mr. Sumit Kumar Debnath Male IIT Kharagpur West Bengal PhD IIT Kharagpur 2012  
18 3511 Mr Saurabh Kumar Singh Male TIFR Maharashtra PhD IIT Kanpur,M.Sc. 2010  
19 3558 Mr Balesh  Kumar Male Harish-Chandra Research Institute Uttar Pradesh PhD Banaras Hindu Univ. 2011  
20 3559 Ms. Miss  Rakvi Female Um-Dae Cebs Centre For Excellence In Basic Sciences Maharashtra Student Um-Dae Cebs Centre For Excellence In Basic Sciences NA  
21 3561 Mr. Pranabesh  Das Male ISI, New Delhi   Junior Research Fellow (2ND  Year) Ramakrishna Mission Vivekananda Univ. , Belur Math, Howrah 2011  
22 3581 Mr Mani  Kandan Male Harish chandra research institute Uttar Pradesh PhD Student Bharathidasan Univ. , Trichy 2011  
23 3599 Ms. Divyum  Sharma Female TIFR Maharashtra PhD IIT, Delhi 2011  
24 3609 Dr. Pratha Anuradha Kameswari Female Andhra Univ. Andhra Pradesh Asst. Prof. Univ.  of Hyderabad 1993 4 Mar 2000
25 3612 Dr. Brajesh Kumar Sharma Male Univ.  of Allahabad Uttar Pradesh Asst. Prof. Univ.  of Allahabad 1994 9 Dec 2006
26 3613 Mr Tushar Kanta Naik Male CMI Tamil Nadu M.Sc Student Chennai Mathematical Institute NA  
27 3615 Mr Manoj  Kumar Male Univ. of Lethbridge Lethbridge, Canada Graduate Student Panjab Univ. 2007  
Local Participants
1 2885 Mr. Abhash Kumar Jha Male NISER, Bhubaneswar Orissa Ph.D. Student Banaras Hindu Univ. 2010  
2 3407 Ms. Madhusmiita  Sahoo Female KIIT Univ. Orissa Asst. Prof. Utkal Univ. 2001  
3 3408 Dr. Punam  Gupta Female KIIT Univ. Orissa Asst. Prof. Banaras Hindu Univ. 2007 15 Mar 2012
4 3450 Mr. Ankush  Goswami Male NISER Orissa MSc Student NISER  Appeared/ Awaiting Result  
5 3567 Mr Nabin Kumar Meher Male KIIT Univ. Orissa Asst. Prof. IIT Kanpur 2011  
6 3598 Mr. Utpal Chandra De Male KIIT Univ. Orissa Asst. Prof. North Orissa Univ. 2006  
7 NA Dr. Prashant Kumar Ray Male