Research Interests:
The broad areas of my research are Number Theory, Algebra, and Cryptography.
In particular, I am interested in Algebraic Varieties, Hypergeometric functions, p-Adic Analysis, Supercongruences, Apery-like Numbers, Modular Forms, Exponential sums, Supercharacter theory, Evaluation of determinants involving residues, Hankel Determinants, and Permutation Polynomials.
Google Scholar Profile: Citations: 258, h-index: 8, i-10 index: 7.
Scopus Profile: Citations: 211, h-index: 7, i-10 index: 7.
ORCID ID: https://orcid.org/0000-0002-9242-3611
MR Author ID: 981394
Publications:
42. Gautam Kalita & R. Chaliha, Determinants of cyclotomic matrices and their connections to hypergeometric functions and algebraic curves, Under review.
41. Gautam Kalita & R. Chaliha, Concerning some determinants involving quadratic residues, Under review.
40. S. Azharuddin & Gautam Kalita, Certain transformations for Appell series over finite fields and a generalized Apery-like number, Under review.
39. F. Sayed & Gautam Kalita, A supercharacter theory on (Z/pZ)^3 and 2-dimensional Kloosterman sums, Under review.
38. Gautam Kalita & R. Chaliha, On some generalized determinants involving Legendre symbols, Under review.
37. R. Chaliha & Gautam Kalita, On some conjectural determinants of Sun involving residues, Under review.
36. S. Azharuddin & Gautam Kalita, p-adic F_3-Appell series and a family of algebraic curves, Under review.
35. Gautam Kalita & F. Sayed, Fifth degree mixed moment of Kloosterman sums, supercharacter theory, and elliptic curves, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., https://doi.org/10.1007/s40010-025-00950-x (2025).
34. S. Azharuddin & Gautam Kalita, Traces of Frobenius for elliptic curves and Appell series in p-adic settings, Int. J. Number Theory, Accepted for publication.
33. A. S. Chetry & Gautam Kalita, Lauricella hypergeometric series F_B^(n) over finite fields, J. Ramanujan Math. Soc. 40 (4), 433--443 (2025). [Q4, SCI Expanded, IF: NA]
32. S. Azharuddin & Gautam Kalita, F_4-Appell series in p-adic settings and their connections to algebraic curves, J. Math. Anal. Appl. 551 (1), Art. no. 129601, pp. 21 (2025), Elsevier. [Q1, SCI Expanded, Scopus, 2024 IF: 1.2]
31. Gautam Kalita & S. Azharuddin, A transformation and certain values for hypergeometric series over finite fields, The Ramanujan J. 66, Art no. 33, pp 15 (2025), Springer. [Q1, SCI Expanded, Scopus, 2023 IF: 0.6].
30. Gautam Kalita, S. Azharuddin, & F. Sayed, A summation transformation formula for Gaussian hypergeometric series and twisted Kloosterman sheaf sums, Res. Number Theory, 11, Art. no. 22, pp. 11 (2025), Springer. [Q2, Scopus, 2023 IF: 0.6].
29. S. Azharuddin & Gautam Kalita, A family of algebraic curves and Appell series over finite fields, The Ramanujan J. 64, 823--834 (2024), Springer. [Q1, SCI Expanded, Scopus, 2023 IF: 0.6].
28. F. Sayed & Gautam Kalita, On a supercharacter analog of nilpotent groups, Comm. Algebra 52 (1), 443--449 (2024), Taylor & Francis. [Q2, SCI Expanded, Scopus, 2022 IF: 0.7].
27. Gautam Kalita & S. Azharuddin, Transformations for Appell series over finite fields and traces of Frobenius for elliptic curves, Finite Fields Appl. 92, Art no. 102301, pp. 29 (2023), Elsevier. [Q1, SCI, Scopus, 2019 IF: 1.478].
26. F. Sayed & Gautam Kalita, Moments of mixed Kloosterman sums, supercharacters, and elliptic curves, The Ramanujan J. 63, 161--176 (2023), Springer. [Q1, SCI Expanded, Scopus, 2023 IF: 0.6].
25. F. Sayed & Gautam Kalita, Moments of Kloosterman sums, supercharacters, and elliptic curves, Indian J. Pure Appl. Math. 54, 200–209 (2023), Springer. [Q3, SCI Expanded, Scopus, 2021 IF: 0.559].
24. A. S. Chetry & Gautam Kalita, Lauricella hypergeometric series F_A^(n) over finite fields, The Ramanujan J. 57, 1335 1354 (2022), Springer. [Q2, SCI Expanded, Scopus, 2021 IF: 0.804].
23. A. Jana & Gautam Kalita, Supercongruences motivated by some generalized VanHamme type congruences, Res. Number Theory 8, Article 54, pp (2022), Springer. [Q3, Scopus, IF: NA].
22. F. Sayed & Gautam Kalita, Eighth power moment of Kloosterman sums and elliptic curves via supercharacters, The Ramanujan J. 58, 801–814 (2022), Springer. [Q2, SCI Expanded, Scopus, 2021 IF: 0.804].
21. A. S. Chetry, A. Jana, & Gautam Kalita, Proof of a supercongruence conjecture of Bing He, Res. Number Theory 7, Article 21, pp. 8 (2021), Springer. [Q2, Scopus, IF: NA].
20. Gautam Kalita & A. Jana, Certain character sums, Gaussian hypergeometric series, and their connections to algebraic curves, Finite Fields Appl. 72, Article 101832 , pp. 18 (2021), Elsevier. [Q1, SCI, Scopus, 2019 IF: 1.478].
19. A. Jana & Gautam Kalita, On some conjectural supercongruences for sums involving certain rising factorials, Results Math. 76, Article 155, pp. 10 (2021), Springer. [Q1, SCI Expanded, Scopus, 2019 IF: 1.162].
18. Gautam Kalita & A. Jana, On some supercongruence conjectures for truncated hypergeometric series, Indian J. Pure Appl. Math. 52, 168–192 (2021), Springer. [Q3, SCI Expanded, Scopus, 2018 IF: 0.337].
17. Gautam Kalita, Another proof of a supercongruence conjecture of Z.-W. Sun, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 91 (2), 2853–287 (2021), Springer. [Q4, SCI Expanded, Scopus, 2017 IF: 0.679].
16. A. Jana & Gautam Kalita, Proof of some conjectural supercongruences of Guo and Schlosser, The Ramanujan J. 54, 649–658 (2021), Springer. [Q2, SCI Expanded, Scopus, 2017 IF: 0.711].
15. A. Jana & Gautam Kalita, Supercongruences for sums involving fourth power of some rising factorials, Proceedings: Math. Sci. 130, Article 59, pp. 13 (2020), Springer. [Q3, SCI Expanded, Scopus, 2018 IF: 0.318].
14. A. S. Chetry & Gautam Kalita, On a general Van Hamme-type supercongruence, J. Ramanujan Math. Soc. 35 (4), 347–355 (2020). [Q3, SCI Expanded, IF: NA].
13. A. S. Chetry & Gautam Kalita, More supercongruences for generalized Apery number, J. Comb. Number Theory 10 (3), 169–181 (2019), Nova Publications.
12. A. Jana & Gautam Kalita, Supercongruences for sums involving rising factorial (1/l)^3, Integral Transforms Spec. Funct. 30 (9), 683–692 (2019), Taylor & Francis. [Q2, SCI Expanded, Scopus, IF: NA].
11. Gautam Kalita & A. S. Chetry, On some supercongruences concerning truncated hypergeometric series, Proc. Amer. Math. Soc. 147 (2), 533–546 (2019), AMS. [Q1, SCI, SCI Expanded, 2017 IF: 0.679].
10. Gautam Kalita, Beukers-like supercongruences for generalized Ap´ery numbers, The Ramanujan J. 47 (3), 501–508 (2018), Springer. [Q1, SCI Expanded, Scopus, 2017 IF: 0.711].
9. Gautam Kalita, Values of Gaussian hypergeometric series and their connections to algebraic curves, Int. J. Number Theory 14 (1), 1–18 (2018), World Scientific. [Q2, SCI Expanded, Scopus, 2014 IF: 0.462].
8. Gautam Kalita & A. S. Chetry, Congruences for generalized Ap´ery numbers and Gaussian hypergeometric series, Res. Number Theory 3, Article 5, pp. 15 (2017), Springer. [Q2, Scopus, IF: NA].
7. R. Barman & Gautam Kalita, Hyperelliptic curves over Fq and Gaussian hypergeometric series, J. Ramanujan Math. Soc. 30 (3), 331–348 (2015). [Q3, SCI Expanded, IF: NA].
6. R. Barman, Gautam Kalita, & N. Saikia, Hyperelliptic curves and values of Gaussian hypergeometric series, Archiv der Mathematik (Basel) 102 (4), 345–355 (2014), Springer. [Q2, SCI Expanded, 2017 IF: 0.590].
5. R. Barman & Gautam Kalita, Hypergeometric functions over Fq and traces of Frobenius for elliptic curves, Proc. Amer. Math. Soc. 141 (10), 3403–3410 (2013), AMS. [Q1, SCI, SCI Expanded, 2017 IF: 0.679].
4. R. Barman & Gautam Kalita, Elliptic Curves and Special Values of Gaussian hypergeometric series, J. Number Theory 133 (9), 3099–3111 (2013), Elsevier. [Q2, SCI Expanded, Scopus, 2017 IF: 0.774].
3. R. Barman & Gautam Kalita, On the polynomial equation x^d+ax+b = 0 and Gaussian hypergeometric series, Int. J. Number Theory 9 (7), 1753–1763 (2013), World Scientific. [Q1, SCI Expanded,Scopus, 2014 IF: 0.462].
2. R. Barman & Gautam Kalita, Certain values of Gaussian hypergeometric series anda family of algebraic curves, Int. J. Number Theory 8 (4), 945–961 (2012), World Scientific. [Q2, SCI Expanded, Scopus, 2014 IF: 0.462].
1. R. Barman & Gautam Kalita, Hypergeometric functions and a family of algebraic curves, The Ramanujan J. 28 (2), 175–185 (2012), Springer. [Q2, SCI Expanded, Scopus, 2017 IF: 0.711].
Ph.D. Students at IIIT Guwahati:
Rituparna Chaliha: Joined in September, 2022 as a CSIR-JRF.
Proposed work: Evaluations of determinants involving residues.
Present Position: Assistant Professor, Department of Mathematics, Assam Engineering College, Guwahati.
Shaik Azharuddin: Joined on 14th August, 2021 as a UGC-JRF, Submitted on 23rd June 2025, Thesis Defended on 31st July 2025..
Title of the Thesis: Hypergeometric series and Appell series over finite fields and in p-adic settings, and their connections to algebraic curves.
Present Position: UGC Senior Research Fellow.
Fahim Sayed: Joined on 24th August 2020 as a CSIR-JRF, Submitted on 27th November 2024, Thesis Defended on 23rd July 2025.
Title of the thesis: Supercharacter analog of nilpotent groups and supercharacter theories in the study of Kloosterman sums.
Present Position: Assistant Professor, Department of Mathematics, Bhola Nath College, Dhubri, Assam (Sept 2022--).
Arijit Jana: Joined on 17th July 2017 as an INSPIRE-JRF, Submitted on 26th May 2021, Thesis Defended on 26 August 2021.
Title of the thesis: Some conjectural supercongruences for truncated hypergeometric series.
Present Position: Assistant Professor, Department of Mathematics, NIT Silchar (Nov 2023--).
Previous Positions: (a) Research Associate, ISI Tezpur, North-East Centre (Nov 2021--Jan 2022).
(b) Post Doctoral Fellow, HRI, Prayagraj (Feb 2022--July 2023).
Arjun Singh Chetry: Joined on 14th January 2016 as an Institute Fellow, Submitted on 18th September 2020, Thesis defended on 28th January 2021.
Title of the thesis: Generalized Apery numbers, hypergeometric functions, and related supercongruences.
Present Position: Assistant Professor, Department of Mathematics, Digboi College, Tinsukia, Assam.
Reviewing work:
I have been serving as a Reviewer for
Mathematical Reviews, published by the American Mathematical Society, since 2017.
Zentralblatt MATH, published by the European Mathematical Society, the Heidelberg Academy of Sciences and Humanities, and FIZ Karlsruhe, since 2021.
I have been also serving as a Referee of research articles for the following journals:
International Journal of Number Theory (World Scientific).
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (Springer).
Journal of Mathematical Analysis and Applications (Elsevier).
Journal of Symbolic Computation (Elsevier).
Research in the Mathematical Sciences (Springer).
The Ramanujan Journal (Springer).
Integral Transform and Special Functions (Taylor & Francis)