Shifted convolution L-series values for elliptic curves
Abstract Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprisi...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/131415 |
| _version_ | 1826203855656845312 |
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| author | Ali, Asra Mani, Nitya |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ali, Asra Mani, Nitya |
| author_sort | Ali, Asra |
| collection | MIT |
| description | Abstract
Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that
$$\text {genus}(X_0(N)) = 1$$
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| first_indexed | 2024-09-23T12:44:42Z |
| format | Article |
| id | mit-1721.1/131415 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:44:42Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1314152023-03-24T18:12:59Z Shifted convolution L-series values for elliptic curves Ali, Asra Mani, Nitya Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Mathematics Abstract Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that $$\text {genus}(X_0(N)) = 1$$ genus ( X 0 ( N ) ) = 1 . 2021-09-20T17:16:58Z 2021-09-20T17:16:58Z 2018-01-06 2020-09-24T21:09:47Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131415 en https://doi.org/10.1007/s00013-017-1112-6 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer International Publishing AG, part of Springer Nature application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Ali, Asra Mani, Nitya Shifted convolution L-series values for elliptic curves |
| title | Shifted convolution L-series values for elliptic curves |
| title_full | Shifted convolution L-series values for elliptic curves |
| title_fullStr | Shifted convolution L-series values for elliptic curves |
| title_full_unstemmed | Shifted convolution L-series values for elliptic curves |
| title_short | Shifted convolution L-series values for elliptic curves |
| title_sort | shifted convolution l series values for elliptic curves |
| url | https://hdl.handle.net/1721.1/131415 |
| work_keys_str_mv | AT aliasra shiftedconvolutionlseriesvaluesforellipticcurves AT maninitya shiftedconvolutionlseriesvaluesforellipticcurves |