On non-vanishing of certain L-functions
| dc.contributor.author | Shahabi, Shahab | |
| dc.contributor.author | University of Lethbridge. Faculty of Arts and Science | |
| dc.contributor.supervisor | Akbary-Majdabadno, Amir | |
| dc.date.accessioned | 2007-05-12T19:24:42Z | |
| dc.date.available | 2007-05-12T19:24:42Z | |
| dc.date.issued | 2003 | |
| dc.degree.level | Masters | |
| dc.description | vii, 78 leaves ; 29 cm. | en |
| dc.description.abstract | This thesis presents the following: (i) A detailed exposition of Rankin's classical work on the convulsion of two modular L-functions is given; (ii) Let S be the calss Dirichlet series with Euler product on Re(s) > 1 that can be continued analytically to Re(s) = 1 with a possible pole at s = 1. For F,G E S, let F X G be the Euler product convolution of F and G. Assuming the existence of analytic continuation for certain Dirichlet series and some other conditions, it is proved that F x G is non-vanishing on the line Re(s) = 1; (iii) Let Fn be the set of newforms of weight 2 and level N. For f E Fn, let L(sym2f,s) be the associated symmetric square L-function. Let s0=0o + ito with 1 - 1/46 < 0o <1. It is proved that Cs0,EN1-E<#{f E Fn; L (sym2 f, so)=0} for prime N large enough. Here E>0 and Cso,E is a constant depending only on So and E. | en |
| dc.identifier.uri | https://hdl.handle.net/10133/199 | |
| dc.language.iso | en_US | en |
| dc.publisher | Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2003 | en |
| dc.publisher.department | Department of Mathematics and Computer Science | |
| dc.publisher.faculty | Arts and Science | |
| dc.relation.ispartofseries | Thesis (University of Lethbridge. Faculty of Arts and Science) | en |
| dc.subject | L-functions | en |
| dc.subject | Number theory | en |
| dc.subject | Dissertations, Academic | en |
| dc.title | On non-vanishing of certain L-functions | en |
| dc.type | Thesis | en |