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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Heat Traces and Spectral Zeta Functions for $ p$-adic Laplacians

Authors: L. F. Chacón-Cortés and W. A. Zúñiga-Galindo
Original publication: Algebra i Analiz, tom 29 (2017), nomer 3.
Journal: St. Petersburg Math. J. 29 (2018), 529-544
MSC (2010): Primary 11F72, 11S40; Secondary 11F85
Published electronically: March 30, 2018
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Abstract: The study of the heat traces and spectral zeta functions for certain $ p$-adic Laplacians is initiated. It is shown that the heat traces are given by $ p$-adic integrals of Laplace type, and that the spectral zeta functions are $ p$-adic integrals of Igusa type. Good estimates are found for the behavior of the heat traces when the time tends to infinity, and for the asymptotics of the function counting the eigenvalues less than or equal to a given quantity.

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Additional Information

L. F. Chacón-Cortés
Affiliation: Pontificia Universidad Javeriana, Departamento de Matemáticas, Facultad de Ciencias, Cra. 7 No. 43-82, Bogotá, Colombia

W. A. Zúñiga-Galindo
Affiliation: Centro de Investigación y de Estudios Avanzados, Departamento de Matemáticas, Unidad Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, C.P. 76230, Querétaro, QRO, México

Keywords: Heat traces, spectral zeta functions, Minakshisundaram--Pleijel zeta functions, $p$-adic heat equation, $p$-adic functional analysis
Received by editor(s): April 15, 2016
Published electronically: March 30, 2018
Additional Notes: The first author was partially supported by the Grant ID-PPTA: 6646 of the Faculty of Sciences of the Pontificia Universidad Javeriana, Bogotá, Colombia.
The second author was partially supported by Conacyt Grant no. 250845
Article copyright: © Copyright 2018 American Mathematical Society

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