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- W2953783022 abstract "A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for ζ(2m+1). The formula for ζ2(2m+1) is then generalized in two different directions, one, by considering the generalized divisor function σz(n), and the other, by studying a more general analogue of the aforementioned Eisenstein series, consisting of one more parameter N. A number of important special cases are derived from the first generalization. For example, we obtain a series representation for ζ(1+ω)ζ(−1−ω), where ω is a non-trivial zero of ζ(z). We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of ζ(4k−1) and ζ(4k+1) for k∈N." @default.
- W2953783022 created "2019-07-12" @default.
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- W2953783022 date "2019-09-01" @default.
- W2953783022 modified "2023-10-17" @default.
- W2953783022 title "On squares of odd zeta values and analogues of Eisenstein series" @default.
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- W2953783022 doi "https://doi.org/10.1016/j.aam.2019.06.003" @default.
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