Subham Bhakta

activity

20182026

most citedLifting of vector-valued automorphic forms

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

collaborators

18 papers

math.NT2026

Systems of equations with elements of finitely generated groups and with linear recurrence sequences

Subham Bhakta, Alina Ostafe, Igor E. Shparlinski

We obtain new and essentially optimal bounds on the number of solutions of diagonal systems of $k$ polynomial equations in $s$ variables from an arbitrary finite subset of a finite…

math.NT2026

Perfect powers in the product of denominators of elliptic curves

Subham Bhakta

We use sieving arguments to estimate the frequency of $s$ -tuples of rational points $(P_{1}, \dots, P_{s}) \in E_{1} (Q) \times \dots \times E_{s} (Q),$ where $E_{1}, \dots, E_{s}$ …

math.NT2025

Multiplicative dependence in the denominators of points of elliptic curves

Attila Bérczes, Subham Bhakta, Lajos Hajdu +2

Let $E_{1}, \dots, E_{s}$ be $s$ , not necessary distinct, elliptic curves over $Q$ . We give upper bounds on the frequency of $s$ -tuples of points in $E_1(\mathbb{Q})\times \…

math.NT2025

Character sums of Division polynomials twisted by multiplicative functions

Subham Bhakta

Let $E$ be an elliptic curve over the finite field $F_{p}$ , and $P \in E (F_{p})$ be an $F_{p}$ -rational point. We obtain nontrivial estimates for multiplicativ…

math.NT2025

On the correlations between character sums of division polynomials under shifts

Subham Bhakta, Igor E. Shparlinski

Let $E$ be an elliptic curve over the finite field $F_{p}$ , and $P \in E (F_{p})$ be an $F_{p}$ -rational point. We study the sums \[ S_{χ,P}(N,h) = \sum_{n=1}^N…

math.NT2025

On quantum ergodicity for higher dimensional cat maps modulo prime powers

Subham Bhakta, Igor E. Shparlinski

A discrete model of quantum ergodicity of linear maps generated by symplectic matrices $A \in Sp (2 d, Z)$ modulo an integer $N \geq 1$ , has been studied for $d = 1$ and…

math.NT2024

Exponential Sums with Sparse Polynomials and Distribution of the Power Generator

Subham Bhakta, Igor Shparlinski

We obtain new bounds on complete rational exponential sums with sparse polynomials modulo a prime, under some mild conditions on the degrees of the monomials of such polynomials. T…

math.NT2024

On an indivisibility version of Iizuka's conjecture

Muneeswaran R, Srilakshmi Krishnamoorthy, Subham Bhakta

Iizuka's conjecture predicts that, given $m \in N$ and a prime $p$ , there exists infinitely many integers $n$ such that the class numbers of \textit{all} of the following…

math.NT2024

Watkins's conjecture for elliptic curves with a rational torsion

Subham Bhakta, Srilakshmi Krishnamoorthy

Watkins's conjecture suggests that for an elliptic curve $E / Q$ , the rank of the group $E (Q)$ of rational points is bounded above by $ν_{2} (m_{E})$ , where $m_{E}$ is th…

math.NT2023

Modular degree and a conjecture of Watkins

Subham Bhakta, Srilakshmi Krishnamoorthy, Sunil Kumar Pasupulati

Given an elliptic curve $E / Q$ of conductor $N$ , there exists a surjective morphism $ϕ_{E} : X_{0} (N) \to E$ defined over $Q$ . In this article, we discuss the growth of…

math.NT2023

Congruence classes for modular forms over small sets

Subham Bhakta, S. Krishnamoorthy, R. Muneeswaran

J.P. Serre showed that for any integer $m, a (n) \equiv 0 (mod m)$ for almost all $n,$ where $a (n)$ is the $n^{th}$ Fourier coefficient of any modular form with rational coeff…

math.NT2022★ 1 cited

Lifting of vector-valued automorphic forms

Jitendra Bajpai, Subham Bhakta

Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vecto…

math.NT2021

The elliptic sieve and Brauer groups

Subham Bhakta, Daniel Loughran, Simon L. Rydin Myerson +1

A theorem of Serre states that almost all plane conics over $Q$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves…

math.NT2021★ 1 cited

Galois representations and composite moduli

Subham Bhakta

It is known that for any elliptic curve $E / Q$ and any integer $m$ co-prime to $30,$ the induced Galois representation $ρ_{E,m}: \text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}…

math.NT2020

Growth of Fourier coefficients of vector-valued automorphic forms

Jitendra Bajpai, Subham Bhakta, Renan Finder

In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated to even integer weight vector-valued automorphic forms of Fuchsian groups…

math.NT2020

Exponential sums in prime fields for modular forms

Jitendra Bajpai, Subham Bhakta, Victor C. Garcia

The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. Th…

math.NT2020

Distribution of Non-Wieferich primes in certain algebraic groups under ABC

Subham Bhakta

Under ABC, Silverman showed that there are infinitely many non-Wieferich primes with respect to any (non-trivial) base $a$ . Recently Srinivas and Subramani proved an analogous resu…

math.NT2018

Virtual characters on L-functions

Subham Bhakta

In this expository note we show the inception and development of the Heilbronn characters and their application to the holomorphy of quotients of Artin L-functions. Further we use…