Tau function: Difference between revisions
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:<math> \sum_n \tau(n) n^{-s} = \prod_p \left(1 - \tau(p) p^{-s} + p^{11-2s} \right)^{-1} .\,</math> | :<math> \sum_n \tau(n) n^{-s} = \prod_p \left(1 - \tau(p) p^{-s} + p^{11-2s} \right)^{-1} .\,</math> | ||
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Latest revision as of 06:01, 25 October 2024
In mathematics, Srinivasa Ramanujan's tau function is an arithmetic function which may defined in terms of the Delta form by the formal infinite product
Since Δ is a Hecke eigenform, the tau function is multiplicative, with formal Dirichlet series and Euler product