Prabhakar Yadav

collaborators

5 papers

math.NT2026

Power Integral Bases in Polynomial Compositions

Aakash Choudhary, Supriya Pisolkar, Prabhakar Yadav

In this paper, we study the monogeneity of a special class of composed polynomials of the form $(f \circ g) (x) = (x^{m} + c)^{n} + a (x^{m} + c)^{n - 1} + d (x^{m} + c)^{n - 2} + b,$ where \( f…

math.NT2026

Monogenic Fields from Polynomial Compositions with Applications

Anuj Jakhar, Ravi Kalwaniya, Prabhakar Yadav

A number field $K$ is called \emph{monogenic} if its ring of integers $Z_{K}$ can be expressed as a simple ring extension $Z [I^\pm]$ for some $I^\pm \in Z_{K}$ . A m…

math.NT2026

Arithmetic Aspects of Number Fields Generated by Polynomial Families

Rupam Barman, Anuj Jakhar, Ravi Kalwaniya +1

Let $f (x) = (x^{k} + c)^{m} - a x^{n} \in Z [x]$ be an irreducible polynomial over $Q$ , where $k, m, n \in N$ with $k m > n$ , and let $K = Q (I^¸)$ , where $I^¸$ is a…

math.NT2025

Behaviour of Newton Polygon over polynomial composition

Anuj Jakhar, Shanta Laishram, Kotyada Srinivas +1

In this paper, we study the structure of Newton polygons for compositions of polynomials over the rationals. We establish sufficient conditions under which the successive vertices…

math.NT2025

Primitive prime divisors in the forward orbit of a polynomial

Shanta Laishram, Sudhansu S. Rout, Prabhakar Yadav

For the polynomial $f (z) \in Q [z]$ , we consider the Zsigmondy set $Z (f, 0)$ associated to the numerators of the sequence ${f^{n} (0)}_{n \geq 0}$ . In this paper, w…