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Anupam Saikia

Professor Ph.D. (University of Cambridge, UK)

+91 (0)361 258 2616    a.saikia ◊ iitg ⋅ ac ⋅ in

Research Area: Number Theory
Room No: E-302
Personal Website | IRINS Profile


My area of specialization is Number Theory.

My research interests include


  • Arithmetic of Elliptic Curves,
  • Cyclotomic Fields,
  • Iwasawa Theory,
  • Euler Systems,
  • Formal Groups,
  • P-adic Measures,
  • Galois Cohomology,
  • Permutation Polynomials,
  • Hilbert Polynomials,
  • Class Number


  • PhD:

     Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2001     
Thesis Title:  Iwasawa Theory of Lubin-Tate Division Towers and p-Adic L-Functions
Supervisor: John Coates, FRS, Sadleirian Professor of Mathematics, DPMMS, Cambridge

  • Certificate for Advanced Study in Mathematics (Mathematical Tripos, Part III) at Trinity College, University of Cambridge, 1997 (distinction).
  • The Mathematical Tripos, Trinity College, University of Cambridge, 1996, (wrangler).
  • B.Sc. (Hons.) Mathematics, St. Stephen's College, University of Delhi, 1994 (90.2%).
  • Higher Secondary (XII), Cotton College, Guwahati, 1991 (PCM 93%).
  • High School (X), Govt. Higher Secondary School, Golaghat, Assam, 1989, (86.2%).


  • Associate Dean, Academic Affairs, IIT Guwahati, 2014-17
  • Vice Chairman, JEE Cell, IIT Guwahati, 2013-14
  • Preparatory Coordinator, IIT Guwahati, 2012-13
  • DPPC Secretary, Department of Mathematics, IIT Guwahati, 2011-12


I am teaching MA 542 this semester (Jan-April, 2015).

The other courses that I have taught so far at IIT Guwahati are:

  • Algebra and Number Theory (MA727: PhD course)
  • Linear algebra and Functional Analysis (MA 731: PhD course)
  • Real and Complex Analysis (MA 741: PhD course)
  • Galois Theory (MA 622: MSc elective)
  • Algebraic Number Theory (MA509: MSc elective)
  • Linear Algebra (MA522: MSc))
  • Modern Algebra (MA521: MSc)
  • Differential Equations (MA542: MSc)
  • Modern Algebra (MA222: BTech)
  • Mathematics II (MA102: BTech core course)
  • Mathematics I (MA101: BTech core course)



  • Sir William Hodge Fellowship, awarded jointly by Engineering and Physical Research Council (EPSRC), UK and Institut des Hautes Etudes Scientifiques (IHES), France, 200-2002.
  • Senior Rouseball Scholarship, awarded by Trinity College, Cambridge on the basis of postgraduate research work, 2000-2001.
  • Smith and Knight Prize in the annual mathematics essay competition for second year Ph.D. students at the University of Cambridge, 1999.
  • Research Scholar of Trinity College, the highest category of scholarships of the college open to students, awarded for excellence in Mathematical Tripos - Part III examination, 1997-2000.
  • Overseas Research Scholarship, awarded by the Govt. of UK, 1997-2000.
  • Internal Graduate Studentship, Trinity College, Cambridge, 1997-2000.
  • Senior Scholar of Trinity College, awarded for excellence in Tripos results, 1995-97.
  • Ramanujan Scholarship, awarded annually to one student from India to pursue higher studies in mathematics at the University of Cambridge, 1994-96.
  • Honorary Scholar of Cambridge Commonwealth Trust, 1994-1996.
  • State Merit Scholarship to study mathematics at the University of Delhi, 1991-1994.
  • Ramesh Goel Memorial Prize for the best student of mathematics at St. Stephen's College, 1994.

Journal Publications

22. Shamik Das and Anupam Saikia, "On θ-congruent numbers over real number fields.", Bulletin of Australian Mathematical Society , vol.103 ,pp.218-229, [2021]

21. Anupam Saikia, "On the Iwasawa μ-invariants of supersingular elliptic curves", Acta Aritmetica , vol.194 (2) ,pp.179-186, [2020]

20. Shamik Das and Anupam Saikia, "Families of non-congruent numbers with arbitrarily many pairs of prime factors", Integers , vol.20 [2020]

19. Shamik Das, Debopam Chakraborty and Anupam Saikia, "On the period of the continued fraction of $\sqrt{pq}$.", Acta Aritmetica , vol.196 (3) ,pp.291-302, [2020]

18. Rajesh P. Singh, Bhaba K. Sarma and Anupam Saikia, "A public key crystosystem using a group of permutation polynomials", Tatra Mt. Math. Publ. , vol.77 ,pp.139-162, [2020]

17. Debopam Chakraborty and Anupam Saikia, "On a conjecture of Mordell", Rocky Mountain J. Mathematics , vol.49 (8) ,pp.2545-2556, [2019]

16. Naba Kanta Sarma, Anupam Saikia., "Torsion of elliptic curves over imaginary quadratic fields of class number 1", Rocky Mountain J. Math , vol.48 (8) ,pp.2689-2703, [2018]

15. Anupam Saikia and Kumari Saloni, "Bounding Hilbert coefficients of parameter ideals", Journal of Algebra , vol.67 (142) ,pp.328-344, [2018]

14. Anupam Saikia and Dishari Chaudhuri, "On the derived length of units in group algebra", Czechoslovak Math. J , vol.67 (142) ,pp.855-865, [2017]

13. Debopam Chakraborty and Anupam Saikia, "An explicit construction for unramified quadratic extensions of biquadratic fields.", Acta Arithmetica , vol.178 (2) ,pp.153-161, [2017]

12. Debopam Chakraborty and Anupam Saikia, " Congruence relations for the fundamental unit of a pure cubic field and its class number", Journal of Number theory , vol.166 ,pp.76-84, [2016]

11. Debopam Chakraborty, Saikia Anupam. .. ():-., "On relative class number and continued fractions.", Bull. Korean Math. Soc. , vol.52 (5) ,pp.1559-1568, [2015]

10. Chaudhuri Dishari, Anupam Saikia., "On group algebras with unit groups of derived length at most four", Publ. Math. Debrecen , vol.86 (1-2) ,pp.39-48, [2015]

9. Debopam Chakraborty, Saikia Anupam., "Another look at real quadratic fields of relative class number 1", Acta Arithmetica , vol.163 (4) ,pp.371-377, [2014]

8. Rupam barman and Anupam Saikia, "Iwasawa λ-invariants of p-adic measures on Znp and their Γ-transforms.", Journal of Number Theory , vol.132 (10) ,pp.2258-2266, [2012]

7. A.Saikia, B.K. Sarma, R.P. Singh, "Poly Dragon: An Efficient Multivariate Public Key Cryptosystem", Journal of Mathematical Cryptology. , vol.4 ,pp.349-364, [2011]

6. Rupam Barman and Anupam Saikia, "Iwasawa λ-invariants and Γ-transforms of p-adic measures on Znp", International Journal of Number Theory , vol.8 ,pp.1819-1829, [2010]

5. Anupam Saikia and Rupam Barman, "Coefficients of a p-adic measure on Znp and Iwasawa λ-invariant of its Γ-transform.", Asian-Eur. J. Math. , vol.3 (4) ,pp.545-554, [2010]

4. Rupam Barman and Anuoam Saikia, "A note on Iwasawa μ-invariants of elliptic curves", Bull. Braz. Math. Soc. (N.S.) , vol.41 (3) ,pp.399-407, [2010]

3. Rupam barman and Anupam Saikia, "Iwasawa λ-invariants and Γ-transforms", J. Ramanujan Math. Soc. , vol.24 (2) ,pp.199-209, [2009]

2. A.Saikia., "Selmer Groups of Elliptic Curves with Complex Multiplication.", Canadian Journal of Mathematics. , vol.56 (1) ,pp.194-204, [2004]

1. A.Saikia., "A Simple Proof of a Lemma of Coleman.", Mathematical Proceedings of the Cambridge Philosophical Society. , vol.130 (part 2) ,pp.209-220, [2001]

Conference Publications

3. Anupam Saikia., "Explicit Reciprocity Law of Bloch-Kato and Exponential Maps.", The Bloch-Kato Conjecture for the Riemann Zeta Function, London Mathematical Society Lecture Note Series, Cambridge University Press. ,pp.65-96, [2015]

2. A. Saikia., "Ribet`s Construction of a Suitable Cusp Eigenform.", Workshop on Iwasawa Theory of Totally Real Fields, IIT Guwahati. [2008]

1. A. Saikia., "On units generated by Euler systems.", International Conference on Number Theory, Harish-Chandra Research Institute, Allahabad. [2006]


Currently no current student.


1 Dr. Jaitra Chattopadhyay (NBHM PDF)
2 Dr. Mohit Mishra (NBHM PDF)


1 H Laxmi
2 Ansh Agrawal


1 Shamik Das
2 Rupam Barman
3 Dishari Chaudhuri
4 Debopam Chakraborty
5 Kumari Saloni
6 Naba Kanta Sarma
7 Rajesh Pratap Singh

1. Selmer Groups of Elliptic Curves and Their Applications
Funding Agency : MATRICS, SERB
Principal Investigator: Anupam Saikia
Duration/Starting Year: 2021
Status: Ongoing

2. Web Course: Number Theory
Funding Agency : The Ministry of Human Resource Development, Govt. of India
Principal Investigator: Anupam Saikia
Duration/Starting Year: 2009
Status: Completed

No Project Available!

No Data Available!