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.
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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Banerjee, Pradipto"],"institution":null,"degree_name":"Ph.D.","degree_level":"Campus Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Michael Filaseta"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T04:37:14Z","subjects":["Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["© 2010, Pradipto Banerjee"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarcommons.sc.edu/etd/133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michael Filaseta"]},{"key":"dc:creator","label":"Author","values":["Banerjee, Pradipto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© 2010, Pradipto Banerjee"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarcommons.sc.edu/etd/133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
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.
"]},{"key":"dc:title","label":"Title","values":["On A Conjecture of Pal Turan and Investigations Into Galois Groups of Generalized Laguerre Polynomials"]}]}],"canonical_facts":{"dc:contributor":["Michael Filaseta"],"dc:creator":["Banerjee, Pradipto"],"dc:description.abstract":["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.
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.
"],"dc:identifier":["https://scholarcommons.sc.edu/etd/133"],"dc:rights":["© 2010, Pradipto Banerjee"],"dc:subject":["Mathematics","Physical Sciences and Mathematics"],"dc:title":["On A Conjecture of Pal Turan and Investigations Into Galois Groups of Generalized Laguerre Polynomials"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T04:37:14Z"}