| dc.identifier.uri | http://hdl.handle.net/11401/76412 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | In recent years, substantial progresses have been made towards the development of a general theory of multiple Dirichlet series with functional equations. In this dissertation, we investigate the Shintani zeta function associated to a prehomogeneous vector space and identify it with a Weyl group multiple Dirichlet series. The example under consideration is the set of 2 by 2 by 2 integer cubes, that is the integral lattice in a certain pre-homogeneous vector space acted on by three copies of GL(2). One of M. Bhargava's achievements is the determination of the corresponding integral orbits and the discovery of an extension of the Gauss's composition law for integral binary quadratic forms. We instead consider the action of a certain parabolic subgroup on the same vector space. We show there are three relative invariants that all have arithmetic meanings and completely determine the integral orbits. We prove that the associated Shintani zeta function coincides with the A3 Weyl group multiple Dirichlet series. Lastly, we show that the set of semi-stable integral orbits maps finitely and surjectively to a certain moduli space. The last part of this dissertation is devoted to showing the connection between Shintani zeta functions of PVS and periods of automorphic forms. | |
| dcterms.available | 2017-09-20T16:50:11Z | |
| dcterms.contributor | Takhtajan, Leon | en_US |
| dcterms.contributor | Knapp, Anthony | en_US |
| dcterms.contributor | Starr, Jason | en_US |
| dcterms.contributor | Chinta, Gautam. | en_US |
| dcterms.creator | Wen, Jun | |
| dcterms.dateAccepted | 2017-09-20T16:50:11Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:11Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 64 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76412 | |
| dcterms.issued | 2014-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1
Wen_grad.sunysb_0771E_11858.pdf: 395322 bytes, checksum: d4bf30cf4c89642c8c06ae9b106f1109 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | binary quadratic forms, Gauss's composition law, multiple Dirichlet series, pre-homogeneous vector space, Shintani zeta function, Weyl group multiple Dirichlet series | |
| dcterms.subject | Mathematics | |
| dcterms.title | Shintani Zeta Functions and Weyl Group Multiple Dirichlet Series | |
| dcterms.type | Dissertation | |
