Superimposing theta structure on a generalized modular relation

  title={Superimposing theta structure on a generalized modular relation},
  author={A. Dixit and Rahul Kumar},
  journal={arXiv: Number Theory},
A generalized modular relation of the form $F(z, w, \alpha)=F(z, iw,\beta)$, where $\alpha\beta=1$ and $i=\sqrt{-1}$, is obtained in the course of evaluating an integral involving the Riemann $\Xi$-function. It is a two-variable generalization of a transformation found on page $220$ of Ramanujan's Lost Notebook. This modular relation involves a surprising generalization of the Hurwitz zeta function $\zeta(s, a)$, which we denote by $\zeta_w(s, a)$. While $\zeta_w(s, 1)$ is essentially a product… Expand
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  • 2013
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