A converse theorem for double Dirichlet series and Shintani zeta functions
The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL (2). The c...
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| Format: | Article |
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Mathematical Society of Japan
2014
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| Online Access: | https://eprints.nottingham.ac.uk/34545/ |
| _version_ | 1848794878700421120 |
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| author | Diamantis, Nikolaos Goldfeld, Dorian |
| author_facet | Diamantis, Nikolaos Goldfeld, Dorian |
| author_sort | Diamantis, Nikolaos |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL (2). The converse theorem we prove will apply to a very general family of double Dirichlet series which we now define. |
| first_indexed | 2025-11-14T19:23:12Z |
| format | Article |
| id | nottingham-34545 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:23:12Z |
| publishDate | 2014 |
| publisher | Mathematical Society of Japan |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-345452020-05-04T20:14:50Z https://eprints.nottingham.ac.uk/34545/ A converse theorem for double Dirichlet series and Shintani zeta functions Diamantis, Nikolaos Goldfeld, Dorian The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL (2). The converse theorem we prove will apply to a very general family of double Dirichlet series which we now define. Mathematical Society of Japan 2014-04 Article PeerReviewed Diamantis, Nikolaos and Goldfeld, Dorian (2014) A converse theorem for double Dirichlet series and Shintani zeta functions. Journal of the Mathematical Society of Japan, 66 (2). pp. 449-477. ISSN 1881-1167 Double Dirichlet series Eisenstein series converse theorems forms of half-integral weight http://projecteuclid.org/euclid.jmsj/1398258180 doi:10.2969/jmsj/06620449 doi:10.2969/jmsj/06620449 |
| spellingShingle | Double Dirichlet series Eisenstein series converse theorems forms of half-integral weight Diamantis, Nikolaos Goldfeld, Dorian A converse theorem for double Dirichlet series and Shintani zeta functions |
| title | A converse theorem for double Dirichlet series and Shintani zeta functions |
| title_full | A converse theorem for double Dirichlet series and Shintani zeta functions |
| title_fullStr | A converse theorem for double Dirichlet series and Shintani zeta functions |
| title_full_unstemmed | A converse theorem for double Dirichlet series and Shintani zeta functions |
| title_short | A converse theorem for double Dirichlet series and Shintani zeta functions |
| title_sort | converse theorem for double dirichlet series and shintani zeta functions |
| topic | Double Dirichlet series Eisenstein series converse theorems forms of half-integral weight |
| url | https://eprints.nottingham.ac.uk/34545/ https://eprints.nottingham.ac.uk/34545/ https://eprints.nottingham.ac.uk/34545/ |