Rupam Barman

collaborators

5 papers

math.NT2026

Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms

Sipra Maity, Rupam Barman

Recently, Allen et al. developed the Explicit Hypergeometric Modularity Method (EHMM) that establishes the modularity of a large class of hypergeometric Galois representations in d…

math.NT2026

Arithmetic Aspects of Number Fields Generated by Polynomial Families

Rupam Barman, Anuj Jakhar, Ravi Kalwaniya +1

Let $f (x) = (x^{k} + c)^{m} - a x^{n} \in Z [x]$ be an irreducible polynomial over $Q$ , where $k, m, n \in N$ with $k m > n$ , and let $K = Q (I^¸)$ , where $I^¸$ is a…

math.NT2026

On the discriminant and index of a certain class of polynomials

Rupam Barman, Anuj Narode, Vinay Wagh

Let $f (x) = (x^{2} + 1)^{n} - a x^{n} \in Z [x]$ and assume $f (x)$ is irreducible. Let $I^¸$ be a root of $f (x)$ , set $K = Q (I^¸)$ , and denote by $Z_{K}$ the r…

math.NT2026

On Monogeneity of reciprocal polynomials

Rupam Barman, Anuj Narode, Vinay Wagh

Let $Z_{K}$ denote the ring of integers of the number field $K = Q (I^¸)$ , where $I^¸$ is a root of the monic irreducible polynomial $f (x) \in Z [x]$ . We say t…

math.NT2025

On the Monogenity of Polynomials with Non-Squarefree Discriminants

Rupam Barman, Anuj Narode, Vinay Wagh

In 2012, for any integer $n \geq 2$ , Kedlaya constructed an infinite class of monic irreducible polynomials of degree $n$ with integer coefficients having squarefree discriminants.…