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Article: Central L-values of elliptic curves and local polynomials
| Title | Central L-values of elliptic curves and local polynomials |
|---|---|
| Authors | |
| Keywords | 11F37 11F11 11E76 11M20 (primary) |
| Issue Date | 2020 |
| Publisher | London Mathematical Society. The Journal's web site is located at http://londmathsoc.onlinelibrary.wiley.com/hub/journal/10.1112/(ISSN)1460-244X/ |
| Citation | Proceedings of the London Mathematical Society, 2020, v. 120 n. 5, p. 742-769 How to Cite? |
| Abstract | Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L-functions. In particular, we find finite formulas for certain twisted central L-values of a family of elliptic curves in terms of finite sums over canonical binary quadratic forms. This yields vastly simpler formulas related to work of Birch and Swinnerton-Dyer for such L-values, and extends beyond their framework to special non-CM elliptic curves. |
| Persistent Identifier | http://hdl.handle.net/10722/279178 |
| ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.532 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Ehlen, S | - |
| dc.contributor.author | Guerzhoy, P | - |
| dc.contributor.author | Kane, B | - |
| dc.contributor.author | Rolen, L | - |
| dc.date.accessioned | 2019-10-21T02:21:02Z | - |
| dc.date.available | 2019-10-21T02:21:02Z | - |
| dc.date.issued | 2020 | - |
| dc.identifier.citation | Proceedings of the London Mathematical Society, 2020, v. 120 n. 5, p. 742-769 | - |
| dc.identifier.issn | 0024-6115 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/279178 | - |
| dc.description.abstract | Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L-functions. In particular, we find finite formulas for certain twisted central L-values of a family of elliptic curves in terms of finite sums over canonical binary quadratic forms. This yields vastly simpler formulas related to work of Birch and Swinnerton-Dyer for such L-values, and extends beyond their framework to special non-CM elliptic curves. | - |
| dc.language | eng | - |
| dc.publisher | London Mathematical Society. The Journal's web site is located at http://londmathsoc.onlinelibrary.wiley.com/hub/journal/10.1112/(ISSN)1460-244X/ | - |
| dc.relation.ispartof | Proceedings of the London Mathematical Society | - |
| dc.rights | Proceedings of the London Mathematical Society. Copyright © London Mathematical Society. | - |
| dc.rights | This is the accepted version of the following article: Proceedings of the London Mathematical Society, 2020, v. 120 n. 5, p. 742-769, which has been published in final form at [http://dx.doi.org/10.1112/plms.12305]. | - |
| dc.subject | 11F37 | - |
| dc.subject | 11F11 | - |
| dc.subject | 11E76 | - |
| dc.subject | 11M20 (primary) | - |
| dc.title | Central L-values of elliptic curves and local polynomials | - |
| dc.type | Article | - |
| dc.identifier.email | Kane, B: bkane@hku.hk | - |
| dc.identifier.authority | Kane, B=rp01820 | - |
| dc.description.nature | postprint | - |
| dc.identifier.doi | 10.1112/plms.12305 | - |
| dc.identifier.scopus | eid_2-s2.0-85081205446 | - |
| dc.identifier.hkuros | 307309 | - |
| dc.identifier.volume | 120 | - |
| dc.identifier.issue | 5 | - |
| dc.identifier.spage | 742 | - |
| dc.identifier.epage | 769 | - |
| dc.identifier.isi | WOS:000529680400004 | - |
| dc.publisher.place | United Kingdom | - |
| dc.identifier.issnl | 0024-6115 | - |