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 |
| Published: |
Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/146276 |
| Summary: | 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. |
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