भारतीय प्रौद्योगिकी संस्थान गुवाहाटी

Dr. Rupam Barman

Professor, Department of Mathematics

Publications |

73. Hook length biases in ordinary and t-regular partitions (under review)(with Gurinder Singh) 72. p-Adic hypergeometric functions and certain weight three newforms (under review)(with Sulakashna) 71. On the p-adic valuation of third order linear recurrence sequences (under review)(with Deepa Antony) 70. p-Adic hypergeometric functions and traces of Frobenius of elliptic curves (under review)(with Sulakashna) 69. Cliques of orders three and four in the Paley-type graphs (under review)(with Anwita) 68. A note on Lin's conjecture on PDOt(n)(under review)(with Gurinder Singh) 67. On p-adic denseness of quotients of values of integral forms (under review)(with Deepa Antony and Stevan Gajovic) 66. Arithmetic properties and asymptotic formulae for sigma_0mex(n) and sigma_emex(n), 65. Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions, 64. Number of complete subgraphs of Peisert graphs and hypergeometric functions over finite fields, 63. Number of F_q points on Diagonal hypersurfaces and hypergeometric function, 62. Arithmetic properties of certain t-regular partitions, 61. Divisibility of the partition function PDO_t(n) by powers of 2 and 3, 60. Parity distribution and divisibility of Mex-related partition functions, 59. Hypergeometric functions for Dirichlet characters and Peisert-like graphs on Z_n, 58. Certain Diophantine equations and new parity results for 21-regular partitions, 57. p-Adic quotient sets: linear recurrence sequences, 56. Proofs of some conjectures of Keith and Zanello on t-regular partitions, 55. Certain transformations and values of p-adic hypergeometric functions, 54. p-Adic quotient sets: Diagonal forms, 53. On denseness of certain direction and generalized direction sets, 52. Divisibility of certain ell-regular partitions by 2, 51. p-Adic quotient sets: Cubic forms, 50. Proof of some conjectural congruences of da Silva and Sellers, 49. On a Paley-type graph on Z_n, 48. Certain transformations and special values of hypergeometric functions over finite fields, 47. Higher order moments of generalized quadratic Gauss sums weighted by L-functions, 46. Divisibility of certain singular overpartitions by powers of 2 and 3, 45. On Mex-related partition functions of Andrews and Newman, 44. Certain eta-quotients and arithmetic density of Andrews' singular overpartitions, 43. New density results and congruences for Andrews' singular overpartitions, 42. An improved estimate of the fourth power mean of the general 3-dimensional Kloosterman sums mod p, 41. Mex-related partition functions of Andrews and Newman, 40. Appell series over finite fields and Gaussian hypergeometric series, 39. Summation identities and transformations for hypergeometric series-II, 38. The fourth power mean of the general 4-dimensional Kloosterman sums mod p, 37. Certain product formulas and values of Gaussian hypergeometric series, 36. On Andrews' integer partitions with even parts below odd parts, 35. Appell's hypergeometric series over finite fields, 34. Congruences modulo powers of 2 for overpartition pairs into odd parts, 33. Arithmetic properties of cubic and overcubic partition pairs, 32. Supercongruences for truncated hypergeometric series and p-adic Gamma function, 31. Divisibility of Andrews' singular overpartitions by powers of 2 and 3, 30. Lehmer's generalized Euler numbers in hypergeometric functions, 29. A finite field analogue of the Appell's series F4, 28. New congruences for overpartitions into odd parts, 27. Summation identities and transformations for hypergeometric series, 26. Certain character sums and hypergeometric series, 25. Infinite families of congruences for k-regular overpartitions, 24. Congruences for l-regular overpartitions and Andrew's singular overpartition, 23. Proof of a limited version of Mao's partition rank inequality using a theta function identity, 22. Counting points on Dwork hypersurfaces and p-adic hypergeometric function, 21. Hyperelliptic curves over F_q and Gaussian hypergeometric series, 20. Summation identities and special values of hypergeometric series in the p-adic setting,
19. Certain Transformations for Hypergeometric series in the p-adic setting,
18. p-Adic gamma function and the polynomials x^d+ax+b and x^d+ax^{d-1}+b,
17. p-Adic gamma function and the trace of Frobenius of elliptic curves,
16. On the polynomials x^d+ax^i+b and x^d+ax^{d-i}+b over F_q and Gaussian hypergeometric series,
15. Hyperelliptic curves and values of Gaussian hypergeometric series,
14. On the polynomial x^d+ax+b over F_q and Gaussian hypergeometric series,
13. Another look at Iwasawa lambda-invariants of p-adic measures on (Z_p)^n and Gamma- transforms, 12. Hypergeometric functions over F_q and traces of Frobenius for elliptic curves,
11. Elliptic Curves and Special Values of Gaussian hypergeometric series,
10. Iwasawa lambda-invariants of p-adic measures on (Z_p)^n and their Gamma-transforms,
9. Certain values of Gaussian hypergeometric series and a family of algebraic curves,
8. Hypergeometric functions and a family of algebraic curves,
7. On p-adic Properties of Certain Mahler Coefficients,
6. Iwasawa lambda-invariants and Gamma-transforms of p-adic measures on (Z_p)^n,
5. A note on Iwasawa mu-invariants of Elliptic curves,
4. Coefficients of a p-adic measure on (Z_p)^n and Iwasawa lambda-invariant of its Gamma -transform,
3. Theta Function Identities Associated with Ramanujan's Modular Equations of Degree 15,
2. Iwasawa lambda-invariants and Gamma-transforms, 1. Certain Theta-function Identities and Ramanujan's Modular Equations of Degree 3,
1. Hypergeometric functions over finite fields and their connections to elliptic curves: a survey, |