Veekesh Kumar

activity

20182025

most citedOn inhomogeneous extension of Thue-Roth's type inequality with moving targets

2 citations · 5 across the 11 of their papers we have counts for

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11 papers · 1 filter

math.NT2025

On the rational approximation to linear combinations of powers

Veekesh Kumar, Gorekh Prasad

For a complex number $x$ , $∥ x ∥ := min {∣ x - m ∣ : m \in Z}$ . Let $k \geq 1$ be an integer, and $K$ be a number field. Let $α_{1}, \dots, α_{k}$ be algebraic numbers with $|α_i…

math.NT2025

$S$ -units and period length of continued fractions of linear recursions

Veekesh Kumar, Vivek Singh, Johannes Sprang

Let $(A_{n})_{n \in Z}$ be a linear recurrence sequence with values in a real quadratic field. In this paper, we study the question whether the period length of the continued…

math.NT2025

Algebraic approximations to linear combinations of S-units

Parvathi S Nair, Veekesh Kumar, S. S. Rout

Let $Γ\subset \bar{\Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers, let $α_{1}, \dots, α_{m}$ be non-zero algebraic numbers, and let $ε > 0$ be…

math.NT2025

A simultaneous approximation problem for exponentials and logarithms

Veekesh Kumar, Riccardo Tosi

Let $α_{1}, α_{2}$ be non-zero algebraic numbers such that $\frac{l o g α _{2}}{l o g α _{1}} \in / Q$ and let $β$ be a quadratic irrational number. In this article, we prove that the va…

math.NT2022

Linear independence of values of the $q$ -exponential and related functions

Anup B. Dixit, Veekesh Kumar, Siddhi S. Pathak

In this paper, we establish the linear independence of values of the $q$ -analogue of the exponential function, $E_{q} (x)$ and its derivatives at specified algebraic arguments, when $…

math.NT2022

On the transcendence of growth constants associated with polynomial recursions

Veekesh Kumar

Let $P (x) := a_{d} x^{d} + \dots + a_{0} \in Q [x]$ , $a_{d} > 0$ , be a polynomial of degree $d \geq 2$ . Let $(x_{n})$ be a sequence of integers satisfying \begin{equation*} x_{n+1}=P(x_n)\mbox…

math.NT2022

Sufficient conditions for a problem of Polya

Abhishek Bharadwaj, Veekesh Kumar, Aprameyo Pal +1

Let $α$ be a non-zero algebraic number. Let $K$ be the Galois closure of $Q (α)$ with Galois group $G$ and $Q ˉ$ be the algebraic closure of $Q$ . In t…

math.NT2021★ 2 cited

On inhomogeneous extension of Thue-Roth's type inequality with moving targets

Veekesh Kumar

Let $Γ \subset Q^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $δ, β \in Q^{\times}$ be algebraic numbers with $…

math.NT2020★ 1 cited

On simultaneous approximation of algebraic numbers

Veekesh Kumar, R. Thangadurai

Let $Γ \subset Q ˉ^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $α_{1}, \dots, α_{r} \in Q ˉ^{\times}$ be algebraic numbers which…

math.NT2019★ 2 cited

On Algebraic Conditions for the Non-Vanishing of Linear Forms in Jacobi Theta-Constants

Carsten Elsner, Veekesh Kumar

Elsner, Luca and Tachiya proved in 2019 that the values of the Jacobi-theta constants $θ_{3} (m τ)$ and $θ_{3} (n τ)$ are algebraically independent over $Q$ for distinct integers…

math.NT2018

On the transcendence of certain real numbers

Veekesh Kumar, Bill Mance

In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Hančl and Rucki \cite{hancl…

On the rational approximation to linear combinations of powers

S-units and period length of continued fractions of linear recursions

Algebraic approximations to linear combinations of S-units

A simultaneous approximation problem for exponentials and logarithms

Linear independence of values of the q-exponential and related functions

On the transcendence of growth constants associated with polynomial recursions

Sufficient conditions for a problem of Polya

On inhomogeneous extension of Thue-Roth's type inequality with moving targets

On simultaneous approximation of algebraic numbers

On Algebraic Conditions for the Non-Vanishing of Linear Forms in Jacobi Theta-Constants

On the transcendence of certain real numbers

$S$ -units and period length of continued fractions of linear recursions

Linear independence of values of the $q$ -exponential and related functions