# Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations

```@article{Dixit2013SelfreciprocalFP,
title={Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations},
author={Atul Dixit and Victor H. Moll},
journal={Journal of Number Theory},
year={2013},
volume={147},
pages={211-249}
}```
• Published 2013
• Mathematics, Physics
• Journal of Number Theory
Abstract Integrals containing the first power of the Riemann Ξ-function as part of the integrand that lead to modular-type transformations have been previously studied by Ramanujan, Hardy, Koshlyakov, Ferrar and others. An integral containing the square of the Riemann Ξ-function and involving an extra parameter z, whose type naturally extends that of the afore-mentioned integrals, was studied by Ramanujan. This integral implicitly involves squaring of the functional equation of ζ ( s ) . A… Expand
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