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University of South Carolina
On A Conjecture of Pal Turan and Investigations Into Galois Groups of Generalized Laguerre Polynomials
Abstract
dc:description.abstract<p>In this dissertation we consider two problems. The first problem concerns a conjecture of Pal Turan on distance of a polynomial with integer coefficients from irreducible polynomial. Th problem remains open for polynomials with degree greater than 35. A. Schinzel, in 1970, reformulated Turan's conjecture and subsequently proved the same. In the first part of this dissertation we give a refinement of Schinzel's result.</p> <p>In the second half we investigate the Galois groups associated with the generalized Laguerre polynomials. We are able to classify Laguerre polynomials with the alternating group as the Galois group. We further compute the Galois groups in certain particular cases.</p>
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Campus Access Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Year
- 2010
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Banerjee, Pradipto
- Contributors dc:contributor
-
- Michael Filaseta
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- © 2010, Pradipto Banerjee
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholarcommons.sc.edu/etd/133
- OAI identifier oai:identifier
- oai:scholarcommons.sc.edu:etd-1134