arXiv subjects

Rudranarayan Padhy

Publications and source records attributed to Rudranarayan Padhy.

3 recordsLinked to original sources

arXiv2026

Quantitative bounds on integrality for post-critically finite maps

Let $K$ be a number field with algebraic closure $\overline{K}$ and let $S$ be a finite set of places of $K$ that contain all the archimedean places. For an integer $d \ge 2$, consider the unicritical polynomial family $f_{d,c}(z) = z^d + c$. Recently, Benedetto and Ih studied the distribution of post-critically finite parameters $c$ that are $S$-integral relative to a fixed point $\alpha \in \overline{K}$ such that $f_{d, \alpha}$ is not post-critically finite. In this paper, we study the quantitative aspects of their result. In particular, under some additional assumptions we establish quantitative bounds on the number of $S$-integral post-critically finite parameters in the generalized Mandelbrot set $\mathcal{M}_{d, v}$ relative to a non post-critically finite parameter $\alpha$ as $\alpha$ varies over number fields of bounded degree.

math.NT↗

arXiv2024

Uniform bounds on $S$-integral preperiodic points for chebyshev polynomials

Let $K$ be a number field with algebraic closure $\bar{K}$, let $S$ be a finite set of places of $K$ containing the archimedean places, and let $φ$ be Chebyshev polynomial. In this paper we prove uniformity results on the number of $S$-integral preperiodic points relative to a non-preperiodic point $β$, as $β$ varies over number fields of bounded degree.

math.NT↗

arXiv2024

Sum of terms of recurrence sequences in the solution sets of generalized Pell equations

Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that sums of two terms recurrence sequences in the solution sets of generalized Pell equations are infinitely many. Further, we give an upper bound for the number of such terms when there are only finitely many of them. This work is motivated by the recent paper Hajdu and Sebestyén (Int. J. Number Theory 18 (2022), 1605-1612).

math.NT↗