Kamalakshya Mahatab

activity

20142026

most citedChinese Remainder Theorem for Cyclotomic Polynomials in

Z [X]

4 citations · 6 across the 14 of their papers we have counts for

collaborators

22 papers

math.NT2026

Omega bounds for the Piltz divisor problem

Nilmoni Karak, Kamalakshya Mahatab

We improve our earlier omega bounds for the error term in the Piltz divisor problem over number fields. Our proof uses a weighted extension of a counting theorem of Balasubramanian…

math.CO2026

Zeros in The Character Table of The Wreath Product of The Symmetric Group

Jayanta Barman, Kamalakshya Mahatab

Let $G$ be a finite group with $t$ conjugacy classes, and let $S_{N}$ be the symmetric group. Let $Z_{t} (N)$ be the number of zeros in the character table of the wreath product $G\wr S…

math.NT2026

Sharp lower bounds for shifted moments of Dedekind zeta functions

Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab

Let $K_{1}, \dots, K_{r}$ be fixed number fields, and let $L$ be the compositum of their Galois closures. Assuming GRH for $ζ_{L}$ , we prove a sharp lower bound for products of shifted De…

math.NT2026

Sharp Upper Bounds for Moments of Dedekind Zeta Functions

Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab

Assuming the Generalised Riemann Hypothesis, we establish conjecturally sharp upper bounds for shifted moments of products of Dedekind zeta functions of arbitrary number fields. Th…

math.NT2026

Asymptotic Formula for Multipartitions

Jayanta Barman, Kamalakshya Mahatab

Let $p_{t} (N)$ denote the number of $t$ -multipartitions of a positive integer $N$ . In this article, we obtain an asymptotic formula for $p_{t} (N)$ , when $t ≪ N^{1 - ε}$ , for any $ε>…

math.NT2026

Asymptotic Formula for $(t + 1)$ -Regular Partitions

Jayanta Barman, Kamalakshya Mahatab

A partition is $t$ -regular if none of its parts is divisible by $t$ . Let $p (N, t)$ be the number of $(t + 1)$ -regular partitions of a positive integer $N$ . In 1971, Hagis proved an as…

math.NT2025

The Piltz divisor Problem in Number Fields Using The Resonance Method

Nilmoni Karak, Kamalakshya Mahatab

The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved $Ω -$ bo…

math.NT2025

Lower Bound for The Number of Zeros in The Character Table of The Symmetric Group

Jayanta Barman, Kamalakshya Mahatab

For any two partitions $λ$ and $μ$ of a positive integer $N$ , let $χ_{λ} (μ)$ be the value of the irreducible character of the symmetric group $S_{N}$ associated with $λ$ , evaluated a…

math.NT2025

Omega Results for The Divisor and Circle Problems Using The Resonance Method

Kamalakshya Mahatab

We apply the resonance method to obtain large values of general exponential sums with positive coefficients. As applications, we show improved $Ω$ -bounds for Dirichlet and Piltz di…

math.NT2020

Large values of the argument of the Riemann zeta-function and its iterates

Andrés Chirre, Kamalakshya Mahatab

Let $S (σ, t) = \frac{1}{π} ar g ζ (σ + i t)$ be the argument of the Riemann zeta-function at the point $σ + i t$ in the critical strip. For $n \geq 1$ and $t > 0$ , we define \begin{equation*} S_{n}…

math.NT2020

Joint Extreme values of $L$ -functions

Kamalakshya Mahatab, Łukasz Pańkowski, Akshaa Vatwani

We consider $L$ -functions $L_{1}, \dots, L_{k}$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical…

math.NT2019

Large Oscillations of the Argument of the Riemann Zeta-function

Andrés Chirre, Kamalakshya Mahatab

Let $S (t)$ denote the argument of the Riemann zeta-function, defined as $S (t) = \frac{1}{π} ℑ lo g ζ (1/2 + i t) .$ Assuming the Riemann hypothesis, we prove that $$ S(t)=Ω_{\pm}\bigg…

math.NT2019

Large values of $L$ -functions on $1$ -line

Anup B. Dixit, Kamalakshya Mahatab

In this paper, we study lower bounds of a general family of $L$ -functions on the $1$ -line. More precisely, we show that for any $F (s)$ in this family, there exists arbitrary large…

math.NT2018

Composites In Semirings of Boolean Groups

Kamalakshya Mahatab

We estimate the number of composite elements in the $n$ -th grade of the group semiring of finite boolean groups. In view of this result we may conjecture that the composites in the…

math.NT2018

Omega Theorems for The Twisted Divisor Function

Kamalakshya Mahatab, Anirban Mukhopadhyay

For a fixed $θ \neq = 0$ , we define the twisted divisor function $τ (n, θ) := d ∣ n \sum d^{i θ} .$ In this article we consider the error term $Δ (x)$ in the following asymptotic fo…

math.NT2018★ 1 cited

Large Positive and Negative Values of Hardy's $Z$ -Function

Kamalakshya Mahatab

Let $Z (t) := ζ (\frac{1}{2} + i t) χ^{- \frac{1}{2}} (\frac{1}{2} + i t)$ be Hardy's function, where the Riemann zeta function $ζ (s)$ has the functional equation $ζ(s)=χ(…

math.NT2018

On large values of $L (σ, χ)$

Christoph Aistleitner, Kamalakshya Mahatab, Marc Munsch +1

In recent years a variant of the resonance method was developed which allowed to obtain improved $Ω$ -results for the Riemann zeta function along vertical lines in the critical stri…

math.NT2017

$6$ -th Norm of a Steinhaus Chaos

Kamalakshya Mahatab

We prove that for the Steinhaus Random Variable $z (n)$ \[\mathbb{E}\left(\left|\sum_{n\in E_{N, m}}z(n)\right|^6\right)\asymp |E_{N, m}|^3 \text{ for } m\ll(\log\log N)^{\frac{1}{3…

math.NT2017

Extreme values of the Riemann zeta function on the 1-line

Christoph Aistleitner, Kamalakshya Mahatab, Marc Munsch

We prove that there are arbitrarily large values of $t$ such that $∣ ζ (1 + i t) ∣ \geq e^{γ} (lo g_{2} t + lo g_{3} t) + O (1)$ . This essentially matches the prediction for the optim…

math.NT2016★ 1 cited

Measure Theoretic Aspects Of Error Terms

Kamalakshya Mahatab

This thesis investigates on measure theoretic aspects of fluctuations of error terms appearing in various asymptotic formulas.

math.NT2015

Measure Theoretic Aspects of Oscillations of Error Terms

Kamalakshya Mahatab, Anirban Mukhopadhyay

We consider fluctuations of error terms $Δ (x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $Ω$ an…

math.NT2014★ 4 cited

Chinese Remainder Theorem for Cyclotomic Polynomials in $Z [X]$

Kamalakshya Mahatab, Kannappan Sampath

By the Chinese remainder theorem, the canonical map \[Ψ_n: R[X]/(X^n-1)\to \oplus_{d|n} R[X]/Φ_d(X)\] is an isomorphism when $R$ is a field whose characteristic does not divide $n$ …

Omega bounds for the Piltz divisor problem

Zeros in The Character Table of The Wreath Product of The Symmetric Group

Sharp lower bounds for shifted moments of Dedekind zeta functions

Sharp Upper Bounds for Moments of Dedekind Zeta Functions

Asymptotic Formula for Multipartitions

Asymptotic Formula for (t+1)-Regular Partitions

The Piltz divisor Problem in Number Fields Using The Resonance Method

Lower Bound for The Number of Zeros in The Character Table of The Symmetric Group

Omega Results for The Divisor and Circle Problems Using The Resonance Method

Large values of the argument of the Riemann zeta-function and its iterates

Joint Extreme values of L-functions

Large Oscillations of the Argument of the Riemann Zeta-function

Large values of L-functions on 1-line

Composites In Semirings of Boolean Groups

Omega Theorems for The Twisted Divisor Function

Large Positive and Negative Values of Hardy's Z-Function

On large values of L(σ,χ)

6-th Norm of a Steinhaus Chaos

Extreme values of the Riemann zeta function on the 1-line

Measure Theoretic Aspects Of Error Terms

Measure Theoretic Aspects of Oscillations of Error Terms

Chinese Remainder Theorem for Cyclotomic Polynomials in Z[X]

Asymptotic Formula for $(t + 1)$ -Regular Partitions

Joint Extreme values of $L$ -functions

Large values of $L$ -functions on $1$ -line

Large Positive and Negative Values of Hardy's $Z$ -Function

On large values of $L (σ, χ)$

$6$ -th Norm of a Steinhaus Chaos

Chinese Remainder Theorem for Cyclotomic Polynomials in $Z [X]$