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Algebra i Analiz, 2017, Volume 29, Issue 3, Pages 144–166 (Mi aa1547)  

Research Papers

Heat traces and spectral zeta functions for $p$-adic Laplacians

L. F. Chacón-Cortésa, W. A. Zúñiga-Galindob

a Pontificia Universidad Javeriana, Departamento de Matemáticas, Facultad de Ciencias, Cra. 7 No. 43-82, Bogotá Colombia
b 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

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 behaviour 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.

Keywords: heat traces, spectral zeta functions, Minakshisundaram–Pleijel zeta functions, $p$-adic heat equation, $p$-adic functional analysis.

Funding Agency Grant Number
Pontificia Universidad Javeriana ID-PPTA: 6646
CONACYT - Consejo Nacional de Ciencia y Tecnología 250845
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.


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English version:
St. Petersburg Mathematical Journal, 2018, 29:3, 529–544

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Received: 15.04.2016
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Citation: L. F. Chacón-Cortés, W. A. Zúñiga-Galindo, “Heat traces and spectral zeta functions for $p$-adic Laplacians”, Algebra i Analiz, 29:3 (2017), 144–166; St. Petersburg Math. J., 29:3 (2018), 529–544

Citation in format AMSBIB
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\paper Heat traces and spectral zeta functions for $p$-adic Laplacians
\jour Algebra i Analiz
\yr 2017
\vol 29
\issue 3
\pages 144--166
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\transl
\jour St. Petersburg Math. J.
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\pages 529--544
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