TitleRefinements of Selberg's sieve
NameBlight, Sara Elizabeth (author), Iwaniec, Henryk (chair), Weibel, Charles (internal member), Miller, Stephen (internal member), Chamizo, Fernando (outside member), Rutgers University, Graduate School - New Brunswick,
Selberg trace formula,
DescriptionThis thesis focuses on refinements of Selberg's sieve as well as new applications of the sieve. Sieve methods are addressed in four ways. First, we look at lower bound sieves. We will construct new lower bound sieves that give us non-trivial lower bounds for our sums. The lower bound sieves we construct will give better results than those previously known. Second, we create an upper bound sieve and use it to bound the number of primes to improve Selberg's version of the Brun-Titchmarsh Theorem. We improve a constant in the bound of the number of primes in an arbitrary interval of fixed length. Third, we construct an upper bound sieve to improve the large sieve inequality in special cases. Sieve methods allow us to improve this well-known bound of exponential sums. Finally, we include some notes on the use of successive approximations to give a choice of an upper bound sieve that minimizes the main term and the remainder term simultaneously.
NoteIncludes bibliographical references
Noteby Sara Elizabeth Blight
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.