Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values
Abstract Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities derived earlier in the lit...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/146276 |
| _version_ | 1826204463187099648 |
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| author | Chavan, Parth Chavan, Sarth Vignat, Christophe Wakhare, Tanay |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Chavan, Parth Chavan, Sarth Vignat, Christophe Wakhare, Tanay |
| author_sort | Chavan, Parth |
| collection | MIT |
| description | Abstract
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities derived earlier in the literature, such as the convolution of squares of Bernoulli numbers by Dixit et al., or the Fourier expansion of the convolution of Bernoulli–Barnes polynomials by Komori et al. |
| first_indexed | 2024-09-23T12:55:09Z |
| format | Article |
| id | mit-1721.1/146276 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:55:09Z |
| publishDate | 2022 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1462762023-09-07T04:22:59Z Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values Chavan, Parth Chavan, Sarth Vignat, Christophe Wakhare, Tanay Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Abstract Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities derived earlier in the literature, such as the convolution of squares of Bernoulli numbers by Dixit et al., or the Fourier expansion of the convolution of Bernoulli–Barnes polynomials by Komori et al. 2022-11-10T13:01:01Z 2022-11-10T13:01:01Z 2022-09-01 2022-11-10T04:24:45Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/146276 Chavan, Parth, Chavan, Sarth, Vignat, Christophe and Wakhare, Tanay. 2022. "Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values." en https://doi.org/10.1007/s11139-022-00624-x 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. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature application/pdf Springer US Springer US |
| spellingShingle | Chavan, Parth Chavan, Sarth Vignat, Christophe Wakhare, Tanay Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title | Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title_full | Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title_fullStr | Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title_full_unstemmed | Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title_short | Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values |
| title_sort | dirichlet series under standard convolutions variations on ramanujan s identity for odd zeta values |
| url | https://hdl.handle.net/1721.1/146276 |
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