Dixit, AtulAtulDixitMaji, BibekanandaBibekanandaMaji2025-08-312025-08-312020-04-0110.1017/prm.2018.1462-s2.0-85060551774https://d8.irins.org/handle/IITG2025/23071It is pointed out that the generalized Lambert series studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page 332 of Ramanujan's Lost Notebook in a slightly more general form. We extend an important transformation of this series obtained by Kanemitsu, Tanigawa and Yoshimoto by removing restrictions on the parameters N and h that they impose. From our extension we deduce a beautiful new generalization of Ramanujan's famous formula for odd zeta values which, for N odd and m > 0, gives a relation between ζ(2m + 1) and ζ(2Nm + 1). A result complementary to the aforementioned generalization is obtained for any even N and m ϵ ℤ. It generalizes a transformation of Wigert and can be regarded as a formula for ζ(2m + 1 - 1/N). Applications of these transformations include a generalization of the transformation for the logarithm of Dedekind eta-function η(z), Zudilin- and Rivoal-type results on transcendence of certain values, and a transcendence criterion for Euler's constant γ.falseDedekind eta function | Euler's constant | Lambert series | odd zeta values | Ramanujan's formula | transcendenceArticlehttps://arxiv.org/pdf/1709.0002214737124741-7691 April 202015arJournal14WOS:000524939000008