Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values
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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.
Date issued
2022-09-01Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer SciencePublisher
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."
Version: Author's final manuscript