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On the non-homogeneous quadratic Bessel zeta function

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  26 February 2010

M. Spreafico
M. Spreafico
Affiliation:
Dipartimento Matematica ed Applicazioni, Università Milano Bicocca, Milano, Italy. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CEP 13560-970 São Carlos, SP, Brazil.
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Abstract

This article studies the non-homogeneous quadratic Bessel zeta function ζRB(s, v, a), defined as the sum of the squares of the positive zeros of the Bessel function Jv(z) plus a positive constant. In particular, explicit formulas for the main associated zeta invariants, namely, poles and residua ζRB(0, v, a) and ζRB(0, v, a), are given.

MSC classification

Secondary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 123 - 130
Copyright
Copyright © University College London 2004

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