000			02773nam a22004457a 4500
001			th662
003			ISI Library, Kolkata
005			20251211161439.0
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040			_aISI Library
082	0	4	_223rd _a515.39 _bY12
100	1		_aYadav, Prabhakar Ratipal _eauthor
245	1	0	_aOn some algebraic and dynamical aspects of families of polynomials / _cPrabhakar Ratipal Yadav
260			_aDelhi : _bIndian Statistical Institute, _c2025
300			_a114 p. ;
502			_aThesis (Ph.D.) - Indian Statistical Institute, 2025
504			_aIncludes bibliography
508			_aGuided by Shanta Laishram
520			_aThis thesis investigates several arithmetic and algebraic properties of polynomials, with a particular emphasis on irreducibility, monogenity, and the behaviour of iterated polynomial sequences. We first study truncated binomial polynomials over the rationals and establish new affirmative results concerning their irreducibility. A substantial part of the work develops a detailed analysis of Newton polygons under polynomial composition. These structural insights yield broad applications, including criteria for stability and eventual stability of large families of polynomials, as well as precise information about the degrees and number of irreducible factors appearing in their iterates. These ideas further connect to questions about ramification of primes, provide new directions toward Sookdeo's conjecture, and lead to explicit constructions of towers of number fields that are not monogenic. Further investigations address the monogenity of specific classes of polynomials, providing criteria that characterize when these polynomials generate monogenic extensions. Analytic estimates are also obtained to count such polynomials within the families considered. Finally, we obtain an upper bound for the Zsigmondy set associated with a rational critical point of a polynomial, contributing to the broader understanding of primitive prime divisors in arithmetic dynamics.
650	0		_aTruncated Binomial Polynomials
650	0		_aIrreducibility
650	0		_aValuations
650	0		_aPrimes
650	0		_aPrimitive Prime Divisors
650	0		_aCanonical Height
650	0		_aArithmetic Dynamics
650	0		_aMonogenity
650	0		_aIndex of an Algebraic Integer
650	0		_aPower Basis
650	0		_aRings of Algebraic Integers
650	0		_aNon-Monogenity
650	0		_aGalois Groups
650	0		_aComposition of Polynomials
650	0		_aPolynomial Iteration
650	0		_aStability
650	0		_aEventually Stability
650	0		_aNewton Polygons
856			_uhttps://dspace.isical.ac.in/xmlui/handle/10263/7627?show=full _yLink Text
942			_2ddc _cTH
999			_c437452 _d437452