A conjectural extension of Hecke’s converse theorem
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture...
| Main Authors: | , , , , , , , , |
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| Format: | Journal article |
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Springer US
2017
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| _version_ | 1797105578689953792 |
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| author | Bettin, S Bober, JW Booker, AR Conrey, B Lee, M Molteni, G Oliver, TD Platt, DJ Steiner, RS |
| author_facet | Bettin, S Bober, JW Booker, AR Conrey, B Lee, M Molteni, G Oliver, TD Platt, DJ Steiner, RS |
| author_sort | Bettin, S |
| collection | OXFORD |
| description | We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses. |
| first_indexed | 2024-03-07T06:49:24Z |
| format | Journal article |
| id | oxford-uuid:fc01e6ea-1da9-4750-b5b6-cb9440f952d3 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:49:24Z |
| publishDate | 2017 |
| publisher | Springer US |
| record_format | dspace |
| spelling | oxford-uuid:fc01e6ea-1da9-4750-b5b6-cb9440f952d32022-03-27T13:17:49ZA conjectural extension of Hecke’s converse theoremJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fc01e6ea-1da9-4750-b5b6-cb9440f952d3Symplectic Elements at OxfordSpringer US2017Bettin, SBober, JWBooker, ARConrey, BLee, MMolteni, GOliver, TDPlatt, DJSteiner, RSWe formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses. |
| spellingShingle | Bettin, S Bober, JW Booker, AR Conrey, B Lee, M Molteni, G Oliver, TD Platt, DJ Steiner, RS A conjectural extension of Hecke’s converse theorem |
| title | A conjectural extension of Hecke’s converse theorem |
| title_full | A conjectural extension of Hecke’s converse theorem |
| title_fullStr | A conjectural extension of Hecke’s converse theorem |
| title_full_unstemmed | A conjectural extension of Hecke’s converse theorem |
| title_short | A conjectural extension of Hecke’s converse theorem |
| title_sort | conjectural extension of hecke s converse theorem |
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