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arXiv · 1503.03053

A note on spectral properties of the $p$-adic tree

Slawomir Klimek·Sumedha Rathnayake·Kaoru Sakai
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Abstract

We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\mathbb Z_p$ via Michon's correspondence. We show that the spectrum is closely related to the roots of a certain $q-$hypergeometric function and discuss the analytic continuation of the zeta function associated with $D^*D$.

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Slawomir Klimek, Sumedha Rathnayake, Kaoru Sakai. 2015-03-10. A note on spectral properties of the $p$-adic tree. https://doi.org/10.1063/1.4940339

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