English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, on the complex field $\mathbb{C}$, we prove two integralformulae for the Hankel-Mellin transform and the double Fourier-Mellintransform of Bessel functions, both resulting the hypergeometric function. Astwo applications, we use the former integral formula to make explicit thespectral formula of Bruggeman and Motohashi for the fourth moment of Dedekindzeta function over the Gaussian number field $\mathbb{Q}(i)$ and to establish aspectral formula for the Hecke-eigenvalue twisted second moment of central$L$-values for the Picard group $\mathrm{PGL}_2 (\mathbb{Z}[i])$. Moreover, wedevelop the theory of distributional Hankel transform on $\mathbb{C}\smallsetminus \{0\}$.

On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field