MARC details
| 000 -LEADER |
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02773nam a22004457a 4500 |
| 001 - CONTROL NUMBER |
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th662 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20251211161439.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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251211b |||||||| |||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23rd |
| Classification number |
515.39 |
| Item number |
Y12 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Yadav, Prabhakar Ratipal |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
On some algebraic and dynamical aspects of families of polynomials / |
| Statement of responsibility, etc |
Prabhakar Ratipal Yadav |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Delhi : |
| Name of publisher, distributor, etc |
Indian Statistical Institute, |
| Date of publication, distribution, etc |
2025 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
114 p. ; |
| 502 ## - DISSERTATION NOTE |
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| Dissertation note |
Thesis (Ph.D.) - Indian Statistical Institute, 2025 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliography |
| 508 ## - CREATION/PRODUCTION CREDITS NOTE |
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| Creation/production credits note |
Guided by Shanta Laishram |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This 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# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Truncated Binomial Polynomials |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Irreducibility |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Valuations |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Primes |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Primitive Prime Divisors |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Canonical Height |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Arithmetic Dynamics |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Monogenity |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Index of an Algebraic Integer |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Power Basis |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Rings of Algebraic Integers |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Non-Monogenity |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Galois Groups |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Composition of Polynomials |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Polynomial Iteration |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Stability |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Eventually Stability |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Newton Polygons |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://dspace.isical.ac.in/xmlui/handle/10263/7627?show=full">https://dspace.isical.ac.in/xmlui/handle/10263/7627?show=full</a> |
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Link Text |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
THESIS |
