Subha Sarkar

activity

20142022

most citedA generalization of Tóth identity in the ring of algebraic integers involving a Dirichlet Character

2 citations · 6 across the 15 of their papers we have counts for

collaborators

15 papers

math.AG2022

On Perverse sheaves of a Coxeter hyperplane arrangement of type $A_{n}$

Umesh V Dubey, Subham Sarkar

Kapranov and schechtman gave quiver description of perverse sheaves on real hyperplane arrangements. We used this description to relate the perverse sheaves on Coxeter hyperplane a…

math.AG2022★ 2 cited

The fundamental group and extensions of motives of Jacobians of curves

Subham Sarkar, Ramesh Sreekantan

In this paper we construct extensions of mixed Hodge structures coming from the mixed Hodge structure on the graded quotients of the group ring of the fundamental group of a smooth…

math.NT2022

A Base Change Version of Rasmussen-Tamagawa Conjecture

Plawan Das, Subham Sarkar

We prove a certain uniform version of the Shafarevich Conjecture. As a corollary, we prove the Rasmussen-Tamagawa Conjecture for a particular class of abelian varieties $A$ defined…

math.NT2022★ 1 cited

A generalization of Tóth identity in $F_{q} [T]$ involving a Dirichlet Character

Esrafil Ali Molla, Subha Sarkar

Let $A = F_{q} [T]$ be the polynomial ring over the finite field $F_{q}$ . In this article, we prove a generalization of Tóth identity on $A$ involving…

math.NT2022

Generalization of some weighted zero-sum theorems and related Extremal sequence

Subha Sarkar

Let $G$ be a finite abelian group of exponent $n$ and let $A$ be a non-empty subset of $[1, n - 1]$ . The Davenport constant of $G$ with weight $A$ , denoted by $D_{A} (G)$ , is defined to…

math.AG2021

An Equisingular Specialisation of the Compactified Jacobian and its applications

Sourav Das, A. J. Parameswaran, Subham Sarkar

For any positive integer $k$ , let $X_{k}$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacob…

math.NT2021★ 2 cited

A generalization of Tóth identity in the ring of algebraic integers involving a Dirichlet Character

Subha Sarkar

The $k$ -dimensional generalized Euler function $φ_{k} (n)$ is defined to be the number of ordered $k$ -tuples $(a_{1}, a_{2}, \dots, a_{k}) \in N^{k}$ with $1\leq a_1,a_2,\ldots, a_k \…

math.NT2020

On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character

Jaitra Chattopadhyay, Subha Sarkar

For every positive integer $n$ , Sita Ramaiah's identity states that \medskip \begin{equation*} \sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*} \gcd(a_1+a_2-1,n) = ϕ_2(n)σ_0…

math.NT2018

Distribution of residues modulo $p$ using the Dirichlet's class number formula

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar +1

Let $p$ be an odd prime number. In this article, we study the number of quadratic residues and non-residues modulo $p$ which are multiples of $2$ or $3$ or $4$ and lying in the int…

math.NT2018

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar +1

Let $q \geq 1$ be any integer and let $ε \in [\frac{1}{11}, \frac{1}{2})$ be a given real number. In this short note, we prove that for all primes $p$ satisfying $$ p\equiv 1\pmod{q…

math.CO2018

On determination of Zero-sum $ℓ$ -generalized Schur Numbers for some linear equations

Bidisha Roy, Subha Sarkar

Let $r$ , $m$ and $k \geq 2$ be positive integers such that $r ∣ k$ and let $v \in [0, ⌊ \frac{k - 1}{2 r} ⌋]$ be any integer. For any integer $\ell \in [1, k]…

math.NT2018

On Fractionally Dense Sets

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar

In this article, we prove some subsets of the set of natural numbers $N$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\math…

math.CO2018★ 1 cited

The Determination of 2-color zero-sum generalized Schur Numbers

Aaron Robertson, Bidisha Roy, Subha Sarkar

Consider the equation $E : x_{1} + \dots + x_{k - 1} = x_{k}$ and let $k$ and $r$ be positive integers such that $r ∣ k$ . The number $S_{z, 2} (k; r)$ is defined to be…

math.NT2017

Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

Subham Sarkar

In this paper we construct certain higher Chow cycles in the $K_{1}$ of the Jacobian of Fermat curves, generalising a construction of Collino. We further compute the regulator of t…

math.AG2014

Extensions of Motives and the Fundamental Group

Subham Sarkar, Ramesh Sreekantan

In this paper we construct extensions of the Mixed Hodge structure on the fundamental group of a pointed algebraic curve. These extensions correspond to the regulator of certain ex…

On Perverse sheaves of a Coxeter hyperplane arrangement of type An​

The fundamental group and extensions of motives of Jacobians of curves

A Base Change Version of Rasmussen-Tamagawa Conjecture

A generalization of Tóth identity in Fq​[T] involving a Dirichlet Character

Generalization of some weighted zero-sum theorems and related Extremal sequence

An Equisingular Specialisation of the Compactified Jacobian and its applications

A generalization of Tóth identity in the ring of algebraic integers involving a Dirichlet Character

On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character

Distribution of residues modulo p using the Dirichlet's class number formula

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

On determination of Zero-sum ℓ-generalized Schur Numbers for some linear equations

On Fractionally Dense Sets

The Determination of 2-color zero-sum generalized Schur Numbers

Higher Chow cycles on Jacobian of Fermat curves and Hypergeometric functions

Extensions of Motives and the Fundamental Group

On Perverse sheaves of a Coxeter hyperplane arrangement of type $A_{n}$

A generalization of Tóth identity in $F_{q} [T]$ involving a Dirichlet Character

Distribution of residues modulo $p$ using the Dirichlet's class number formula

On determination of Zero-sum $ℓ$ -generalized Schur Numbers for some linear equations