Some problems in number theory [HBNI Th50]

DSpace/Manakin Repository

Some problems in number theory [HBNI Th50]

Show simple item record

dc.contributor.author Prem Prakash Pandey
dc.date.accessioned 2013-06-06T05:16:40Z
dc.date.available 2013-06-06T05:16:40Z
dc.date.issued 2013-06-06T05:16:40Z
dc.date.submitted 2013
dc.identifier.uri http://hdl.handle.net/123456789/338
dc.description.abstract In this thesis the author has worked on three different problems. Some progress is reported on these three problems. The first problem considered is about "Higher Residue Symbols". Given a finite set S of integers, the question of finding primes p such that each integer, 'a (an element of) S' is a quadratic residue (non-residue) modulo p is dealt by various authors. Many authors including M. Fried and S. Wright have established the infinitude of primes p modulo which each "a an element of S" is a quadratic residue. The density of such primes was considered in for study. The author has generalized the problem and studied the analogous questions. The second problem considered is the Catalan's conjecture / Mihailescu's Theorem. It was conjectured by Eugene Charles Catalan in 1844 that, the only perfect powers among integers which differ by 1 are 8 and 9. As part of this thesis the author studies the equation (x)^p - (y)^q = 1 over a number field K, i.e. when x, y Elements of (O)k. Theory of 'torsion points on elliptic curves' is used to handle the equation when one of the prime is even. The chapter four formulates an appropriate Cassels criteria and prove it partially for imaginary quadratic number fields with class number one. Chapter five reports further progress made on Catalan problem considered here. The author introduces a proper obstruction group, made up of solutions of Catalan problem, and then trap it in a short exact sequence of fairly well studied objects (namely class groups and unit groups). This is pretty analogous to the work in the case of Catalan's conjecture over Z. en_US
dc.publisher.publisher
dc.subject Number Theory en_US
dc.subject HBNI Th 50 en_US
dc.title Some problems in number theory [HBNI Th50] en_US
dc.type.degree Ph.D en_US
dc.type.institution HBNI en_US
dc.description.advisor Balasubramanian, R.
dc.description.pages 83p. en_US
dc.type.mainsub Mathematics en_US

Files in this item

Files Size Format View
HBNI Th50.pdf 603.0Kb PDF View/Open

This item appears in the following Collection(s)

Show simple item record

Search DSpace


Advanced Search

Browse

My Account