Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values
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11139_2022_624_ReferencePDF.pdf
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Author(s)
Chavan, Parth
Chavan, Sarth
Vignat, Christophe
Wakhare, Tanay
Date Issued
September 1, 2022
Publisher
Springer US
Citation
Chavan, Parth, Chavan, Sarth, Vignat, Christophe and Wakhare, Tanay. 2022. "Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values."
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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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.
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DOI of Published Version
https://doi.org/10.1007/s11139-022-00624-x
