Professor Ph.D. (IIT Guwahati)
+91 (0)361 258 2637 rupam ◊ iitg ⋅ ac ⋅ in
Research Area: Number Theory
Room No: E1206
Personal Website  IRINS Profile
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Department Responsibilities:
DFAC, Member
Alumni Matters & External Relations, Member
Department Representative for Institute Research and Development Committee
Algebraic Number Theory, Elliptic Curves, Iwasawa Theory, padic Measures, Exponential Sums, Kloosterman Sums, Hypergeometric Functions over Finite Fields, padic Hypergeometric Series, Modular Forms, Theory of Partitions and the mathematics influenced by Ramanujan
1. Ph. D. : Indian Institute of Technology Guwahati (January 2007 April 2010)
Title of Ph. D. Thesis: Iwasawa Invariants of Elliptic Curves and padic Measures
Thesis Advisor: Professor Anupam Saikia
2. Master of Science (M. Sc.): Indian Institute of Technology Delhi (19992001)
3. Bachelor of Science (B. Sc.): Cotton College, Guwahati (19961999)
1. Professor in the Department of Mathematics, Indian Institute of Technology Guwahati from June 2021 to present
2. Associate Professor in the Department of Mathematics, Indian Institute of Technology Guwahati from July 2016 to June 2021
3. Assistant Professor in the Department of Mathematics, Indian Institute of Technology Delhi from May 2013 to June 2016
4. Associate Professor in the Department of Mathematical Sciences, Tezpur University from August 2010 to May 2013
5. Assistant Professor in the Department of Mathematical Sciences, Tezpur University from October 2002 to August 2010
JulyNov 2023: MA521 Modern Algebra and MA509 Algebraic Number Theory
Courses taught at IIT Guwahati
PG courses
UG courses
Courses taught at IIT Delhi
UG courses
PG courses
PG courses taught at Tezpur University (Central)
1. Editor of The Ramanujan Journal since January 2023.
2. A M Mathai Research Excellence Award for the year 2022 by the Society for Special Functions and their Applications (SSFA).
3. IndoAustrallian visiting fellowship by INSA to work at Newcastle University, Australlia during 20122013 (could not avail).
4. Post doctoral fellowship by the Mathematics Center Heidelberg (MATCH), University of Heidelberg Germany during 2011.
5. Post doctoral fellowship by ICTP Trieste Italy during 2011 (could not avail).
6. Visited School of Mathematics, Tata Institute of Fundamental Research Mumbai from July 23 to August 30, 2008.
During my stay at TIFR, I worked under the supervision of Prof. R. Sujatha.
7. Teacher Fellowship by National Board for Higher Mathematics for a period of three years: 20082011.
8. Junior Research Fellowship by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, December 2000.
9. GATE 2001 in Mathematics with a percentile score of 99.56 and All India Rank: 4.
73. Sulakashna and Rupam Barman, "padic hypergeometric functions and certain weight three newforms", Journal of Mathematical Analysis and Applications , vol.542 ,pp.118, [2025]
72. Rupam Barman, Ajit Singh and Gurinder Singh, "Arithmetic properties of certain tregular partitions", Annals of Combinatorics , vol.28 (2) ,pp.439457, [2024]
71. Rupam Barman, Gurinder Singh and Ajit Singh, "Divisibility of the partition function PDO_t(n) by powers of 2 and 3", Bulletin of Australian Math. Soc. , vol.109 (1) ,pp.1425, [2024]
70. Sulakashna and Rupam Barman, "Number of F_q points on Diagonal hypersurfaces and hypergeometric function", International Journal of Number Theory (accepted) ,pp.117, [2024]
69. S. Bhattacharyya, Rupam Barman, A. Singh, and A. K. Saha, "Parity distribution and divisibility of Mexrelated partition functions", Research in Number Theory , vol.10 ,pp.110, [2024]
68. Anwita Bhowmik and Rupam Barman, "Number of complete subgraphs of Peisert graphs and hypergeometric functions over finite fields", Research in Number Theory , vol.10 ,pp.121, [2024]
67. Sulakashna and Rupam Barman, "Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions", Finite Fields and Their Applications , vol.96 ,pp.130, [2024]
66. Rupam Barman and Gurinder Singh, "Arithmetic properties and asymptotic formulae for sigmaomex(n) and sigmaemex(n) ", The Ramanujan Journal , vol.65 ,pp.125137, [2024]
65. Sulakashna and Rupam Barman, "pAdic hypergeometric functions and the traces of Frobenius of elliptic curves", International Journal of Number Theory (accepted) ,pp.132, [2024]
64. Gurinder Singh and Rupam Barman, "Hook length biases in ordinary and tregular partitions", Journal of Number Theory , vol.264 ,pp.4158, [2024]
63. Anwita Bhowmik and Rupam Barman, "Cliques of orders three and four in the Paleytype graphs", Graphs and Combinatorics , vol.40 (Article No. 80) ,pp.110, [2024]
62. Deepa Antony and Rupam Barman, "padic quotient sets: linear recurrence sequences with reducible characteristic polynomials", Canadian Mathematical Bulletin (accepted) ,pp.110, [2024]
61. Deepa Antony and Rupam Barman, "On the padic valuation of third order linear recurrence sequences", Results in Mathematics (accepted) ,pp.116, [2024]
60. Rupam Barman, Anuj Narode and Vinay Wagh, "On monogenity of certain number fields defined by x^{2.3^sq^}^{r}m", Communications in Algebra (accepted) ,pp.112, [2024]
59. Rupam Barman, Gurinder Singh and Ajit Singh, "Certain Diophantine equations and new parity results for 21regular partitions", Acta Arithmetica , vol.210 ,pp.337351, [2023]
58. Deepa Antony and Rupam Barman, "pAdic quotient sets: linear recurrence sequences", Bulletin of Australian Math. Soc. , vol.108 (1) ,pp.1928, [2023]
57. Anwita Bhowmik and Rupam Barman, "Hypergeometric functions for Dirichlet characters and Peisertlike graphs on Z_n", La Matematica, Journal of the Association for Women in Mathematics , vol.2 (4) ,pp.9921021, [2023] , https://link.springer.com/journal/44007/volumesandissues/24
56. Deepa Antony, Rupam Barman and Jaitra Chattopadhyay, "On denseness of certain direction and generalized direction sets", INTEGERS , vol.22 (Article No. 88) ,pp.19, [2022]
55. Deepa Antony, Rupam Barman and Piotr Miska, "pAdic quotient sets: Diagonal forms", Archiv der Mathematik , vol.119 ,pp.461470, [2022]
54. Sulakashna and Rupam Barman, "Certain transformations and values of padic hypergeometric functions", Research in Number Theory , vol.8 (Article No. 93) ,pp.114, [2022]
53. Ajit Singh and Rupam Barman, "Divisibility of certain ellregular partitions by 2", The Ramanujan Journal , vol.59 ,pp.813829, [2022]
52. Ajit Singh and Rupam Barman, "Proofs of some conjectures of Keith and Zanello on tregular partitions", Pacific Journal of Mathematics , vol.320 (2) ,pp.425436, [2022]
51. R. Barman and M. Tripathi, "Certain transformations and special values of hypergeometric functions over finite fields", The Ramanujan Journal , vol.57 (4) ,pp.12771306, [2022]
50. Deepa Antony and Rupam Barman, "pAdic quotient sets: Cubic forms", Archiv der Mathematik. , vol.118 ,pp.143149, [2022]
49. Ajit Singh and Rupam Barman, "Proof of some conjectural congruences of da Silva and Sellers", Bulletin of Australian Math. Soc. , vol.106 ,pp.5761, [2022]
48. Anwita Bhowmik and Rupam Barman, "On a Paleytype graph on Z_n", Graphs and Combinatorics. , vol.38 (Article No. 41) ,pp.125, [2022]
47. N. Bag and R. Barman, "An improved estimate of the fourth power mean of the general 3dimensional Kloosterman sums mod p", Funct. Approx. Comment. Math. , vol.64 (1) ,pp.3945, [2021]
46. A. Singh and R. Barman, "New density results and congruences for Andrews' singular overpartitions", Journal of Number Theory , vol.229 (12) ,pp.328341, [2021]
45. R. Barman and A. Singh, "Mexrelated partition functions of Andrews and Newman", Journal of Integer Sequences , vol.24 (Article no. 21.6.3) ,pp.112, [2021]
44. M. Tripathi and R. Barman, "Appell series over finite fields and Gaussian hypergeometric series", Research in the Mathematical Sciences , vol.8 (Article No. 28 ) ,pp.134, [2021]
43. N. Bag and R. Barman, "Higher order moments of generalized quadratic Gauss sums weighted by Lfunctions", Asian J. Mathematics , vol.25 (3) ,pp.413430, [2021]
42. R. Barman and A. Singh, "Divisibility of certain singular overpartitions by powers of 2 and 3 ", Bulletin Australian Math. Soc. , vol.104 ,pp.238248, [2021]
41. A. Singh and R. Barman, "Certain etaquotients and arithmetic density of Andrews' singular overpartitions", Journal of Number Theory , vol.229 (12) ,pp.487498, [2021]
40. R. Barman and A. Singh, "On Mexrelated partition functions of Andrews and Newman", Research in Number Theory , vol.7 (Article No. 53) ,pp.111, [2021]
39. R. Barman and N. Saikia, "Supercongruences for truncated hypergeometric series and padic Gamma function", Math. Proc. Cambridge Phil. Soc. , vol.168 (1) ,pp.171195, [2020]
38. C. Ray and R. Barman, "Arithmetic properties of cubic and overcubic partition pairs", The Ramanujan Journal , vol.52 ,pp.243252, [2020]
37. Z. Ahmed, R. Barman and C. Ray, "Congruences modulo powers of 2 for overpartition pairs into odd parts", J. Korean Math. Soc. , vol.57 (2) ,pp.471487, [2020]
36. M. Tripathi, N. Saikia and R. Barman, "Appell's hypergeometric series over finite fields", Int. J. Number Theory , vol.16 (4) ,pp.673692, [2020]
35. C. Ray and R. Barman, "On Andrews' integer partitions with even parts below odd parts", Journal of Number Theory , vol.215 ,pp.321338, [2020]
34. M. Tripathi and R. Barman, "Certain product formulas and values of Gaussian hypergeometric series", Research in Number Theory , vol.6 (Article No. 26) ,pp.129, [2020]
33. N. Bag and R. Barman, "The fourth power mean of the general 4dimensional Kloosterman sums mod p", Research in Number Theory , vol.6 (Article No. 31) ,pp.115, [2020]
32. R. Barman and N. Saikia, "Summation identities and transformations for hypergeometric seriesII", Funct. Approx. Comment. Math. , vol.61 (1) ,pp.742, [2020]
31. R. Barman and T. Komatsu, "Lehmer's generalized Euler numbers in hypergeometric functions", J. Korean Math. Soc. , vol.56 (2) ,pp.485505, [2019]
30. C. Ray and R. Barman, "Divisibility of Andrews' singular overpartitions by powers of 2 and 3", Research in Number Theory , vol.5 (Article No. 22) ,pp.17, [2019]
29. R. Barman and C. Ray, "New congruences for overpartitions into odd parts", Integers , vol.18 (Article No. 50) ,pp.120, [2018]
28. R. Barman and C. Ray, "Congruences for lregular overpartitions and Andrew's singular overpartition", The Ramanujan Journal , vol.45 (2) ,pp.497515, [2018]
27. R. Barman and C. Ray, "Infinite families of congruences for kregular overpartitions", Int. J. Number Theory , vol.14 (1) ,pp.1929, [2018]
26. R. Barman and N. Saikia, "Summation identities and transformations for hypergeometric series", Ann. Math. Quebec , vol.42 (2) ,pp.133157, [2018]
25. R. Barman and N. Saikia, "Certain character sums and hypergeometric series", Pacific Journal of Math. , vol.295 (2) ,pp.271290, [2018]
24. M. Tripathi and R. Barman, "A finite field analogue of the Appell's series F_4", Research in Number Theory , vol.4 (Article No. 35) ,pp.123, [2018]
23. R. Barman, H. Rahman and N. Saikia, "Counting points on Dwork hypersurfaces and padic hypergeometric function", Bulletin Australian Math. Soc. , vol.94 (2) ,pp.208218, [2016]
22. R .Barman and A. Sachdeva, "Proof of a limited version of Mao's partition rank inequality using a theta function identity", Research in Number Theory , vol.2 (Article No. 22) ,pp.16, [2016]
21. R. Barman and N. Saikia, "Certain Transformations for Hypergeometric series in the padic setting", Int. J. Number Theory , vol.11 (2) ,pp.645660, [2015]
20. R. Barman, N. Saikia and D. McCarthy, "Summation identities and special values of hypergeometric series in the padic setting", Journal of Number Theory , vol.153 ,pp.6384, [2015]
19. R. Barman and G. Kalita, "Hyperelliptic curves over F_q and Gaussian hypergeometric series", J. Ramanujan Math. Soc. , vol.30 (3) ,pp.331348, [2015]
18. R. Barman, G. Kalita and N. Saikia, "Hyperelliptic curves and values of Gaussian hypergeometric series", Archiv der Mathematik , vol.102 (4) ,pp.345355, [2014]
17. R. Barman and N. Saikia, "On the polynomials x^d+ax^i+b and x^d+ax^{di}+b over F_q and Gaussian hypergeometric series", The Ramanujan Journal , vol.35 (3) ,pp.427441, [2014]
16. R. Barman and N. Saikia, "pAdic gamma function and the trace of Frobenius of elliptic curves", Journal of Number Theory , vol.140 (7) ,pp.181195, [2014]
15. R. Barman and N. Saikia, "pAdic gamma function and the polynomials x^d+ax+b and x^d+ax^{d1}+b", Finite Fields and Their Applications , vol.29 (9) ,pp.89105, [2014]
14. R. Barman and G. Kalita, "Elliptic Curves and Special Values of Gaussian hypergeometric series", Journal of Number Theory , vol.133 ,pp.30993111, [2013]
13. R. Barman and G. Kalita, "Hypergeometric functions over F_q and traces of Frobenius for elliptic curves", Proc. Amer. Math. Soc. , vol.141 ,pp.34033410, [2013]
12. R. Barman, "Another look at Iwasawa lambdainvariants of padic measures on (Z_p)^n and Gamma transforms", Int. J. Number Theory , vol.9 (5) ,pp.12891299, [2013]
11. R. Barman and G. Kalita, "On the polynomial x^d+ax+b over F_q and Gaussian hypergeometric series", Int. J. Number Theory , vol.9 (7) ,pp.17531763, [2013]
10. R. Barman and G. Kalita, "Hypergeometric functions and a family of algebraic curves", The Ramanujan Journal , vol.28 (2) ,pp.175185, [2012]
9. R. Barman and G. Kalita, "Certain values of Gaussian hypergeometric series and a family of algebraic curves", Int. J. Number Theory , vol.8 (4) ,pp.945961, [2012]
8. R. Barman and A. Saikia, "Iwasawa lambdainvariants of padic measures on (Z_p)^n and their Gammatransforms", Journal of Number Theory , vol.132 ,pp.22582266, [2012]
7. R. Barman, "On padic Properties of Certain Mahler Coefficients", J. Ramanujan Math. Soc. , vol.26 (3) ,pp.195202, [2011]
6. R. Barman and N. Deka Baruah, "Theta Function Identities Associated with Ramanujan's Modular Equations of Degree 15", Proc. Indian Acad. Sci. (Math. Sci.) , vol.120 (3) ,pp.267284, [2010]
5. R. Barman and A. Saikia, "Coefficients of a padic measure on (Z_p)^n and Iwasawa lambdainvariant of its Gamma transform", Asian Eur. J. Mathematics , vol.3 (4) ,pp.545554, [2010]
4. R. Barman and A. Saikia, "A note on Iwasawa muinvariants of Elliptic curves", Bull. Brazilian Math. Soc. , vol.41 (3) ,pp.399407, [2010]
3. R. Barman and A. Saikia, "Iwasawa lambdainvariants and Gammatransforms of padic measures on (Z_p)^n", Int. J. Number Theory , vol.6 (8) ,pp.18191829, [2010]
2. R. Barman and A. Saikia, "Iwasawa lambdainvariants and Gammatransforms", J. Ramanujan Math. Soc. , vol.24 (2) ,pp.199209, [2009]
1. R. Barman and N. Deka Baruah, "Certain Thetafunction Identities and Ramanujan's Modular Equations of Degree 3", Indian J. Mathematics , vol.48 (1) ,pp.113133, [2006]
PostDoc Fellow
1  Dr. Zakir Ahmed 
2  Dr. Sneh Bala Sinha 
3  Dr. Ajit Singh (RA I) 
Research Scholars
1  Deepa Antony 
2  Gurinder Singh 
3  Sulakashna 
4  Alapan Ghosh 
5  Sipra Maity 
1  Ajit Singh 
2  Anwita Bhowmik 
3  Chiranjit Ray 
4  Nilanjan Bag 
5  Mohit Tripathi 
External Research Scholars
1  Subhrajyoti Bhattacharyya (NIT Agartala) 
1  Gautam Kalita (Tezpur University) 
2  Neelam Saikia (IIT Delhi) 
1. Distributions of certain partition functions

2. Elliptic Curves with Complex Multiplication and Hypergeometric Sums

3. Hypergeometric functions, algebraic curves and supercongruences

4. Hypergeometric Functions Over padic Numbers and Algebraic Curves

5. Iwasawa Theory of LubinTate division towers and a lemma of Coleman

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