# On some problems in Additive number theory

 dc.contributor.author Gyan Prakash dc.date.accessioned 2009-11-04T10:46:50Z dc.date.available 2009-11-04T10:46:50Z dc.date.issued 2009-11-04T10:46:50Z dc.date.submitted 2005 dc.identifier.uri http://hdl.handle.net/123456789/138 dc.description.abstract This thesis discusses some problems relating the properties of a set A and those of A+A, when A is a subset of an abelian group. Given a finite abelian group G and A is a subset of G, it is said that A is sum-free if the sets 2A and A are disjoint. Chapter 2 discusses the problem of finding the structure of all large sum-free subsets of G. The complete structure of all largest sum-free subsets of G, are obtained provided all the divisors of order G are congruent to 1 modulo 3. Also partial results are obtained regarding structure of all large maximal sum-free subsets of G. A sum-free set A is maximal if it is not a proper subset of any sum-free set. If there is a divisor of order of G which is not congruent to 1 modulo 3 then structure of all largest sum-free subsets of G was known before. The results in this thesis are based on a recent result of Ben Green and Imre Ruzsa. Chapter 3 improves the 'error term' in asymptotic formula of sigma (G) obtained by Ben Green and Imre Ruzsa, using slight refinement of the methods. Chapter 4 discusses a problem on an additive representation function, using an additive lemma proven by means of graph theory. en_US dc.publisher.publisher dc.subject Algebra en_US dc.subject Sum-free sets en_US dc.title On some problems in Additive number theory en_US dc.type.degree Ph.D en_US dc.type.institution Others en_US dc.description.advisor Balasubramanian, R. dc.description.pages 64p. en_US dc.type.mainsub Mathematics en_US

## Files in this item

Files Size Format View
GyanPraksh.pdf 344.4Kb PDF View/Open