Veekesh Kumar

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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.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

On the transcendence of certain real numbers

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