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On The Index of Polynomial Compositions over Valued Fields
Anuj Jakhar, Ravi Kalwaniya, Shanta Laishram +1
Determining whether an algebraic number field admits a power integral basis is a classical problem, but it can be difficult for fields defined by polynomial compositions and dynami…
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 where \( f…
Monogenic Fields from Polynomial Compositions with Applications
Anuj Jakhar, Ravi Kalwaniya, Prabhakar Yadav
A number field is called \emph{monogenic} if its ring of integers can be expressed as a simple ring extension for some . A mon…
Arithmetic Aspects of Number Fields Generated by Polynomial Families
Rupam Barman, Anuj Jakhar, Ravi Kalwaniya +1
Let be an irreducible polynomial over , where with , and let , where is a ro…
Primitive prime divisors in the forward orbit of a polynomial
Shanta Laishram, Sudhansu S. Rout, Prabhakar Yadav
For the polynomial , we consider the Zsigmondy set associated to the numerators of the sequence . In this paper, w…
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…
A Study of monogenity of Binomial Composition
Anuj Jakhar, Ravi Kalwaniya, Prabhakar Yadav
Let be a root of a monic polynomial of degree . We say is monogenic if it is irreducible over $\Q$ and is a…