Klimek, SlawomirRathnayake, SumedhaSakai, Kaoru2016-09-282016-09-282016Klimek, S., Rathnayake, S., & Sakai, K. (2016). A note on spectral properties of the p-adic tree. Journal of Mathematical Physics, 57(2), 23512. http://doi.org/10.1063/1.4940339https://hdl.handle.net/1805/11034We study the spectrum of the operator D∗D, where the operator D, introduced in Klimek et al. [e-print arXiv:1403.7263v2], is a forward derivative on the p-adic tree, a weighted rooted tree associated to ℤp 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.enPublisher Policyp-adic treezeta functionArticle