Geodesic
Spectral functions of zeros for $q$-Bessel functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 397-414 Cet article a éte moissonné depuis la source Math-Net.Ru

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Zeta functions $\zeta_\nu(z;q)=\sum_{n=1}^{\infty}\bigl[j_{\nu n}(q)\bigr]^{-z}$ and partition functions $Z_\nu(t;q)=\sum_n\exp[-tj_{\nu n}^2 (q)]$ related to the zeros $j_{\nu n}(q)$ of the $q$-Bessel functions $J_\nu(x;q)$ and $J_\nu^{(2)}(x;q)$ are studied. Explicit formulas for $\zeta_\nu(2n;q)$ at $n=\pm 1,\pm 2,\ldots$ are obtained. Poles of $\zeta_\nu(z;q)$ in complex plane and corresponding residues are found. Asymptotics of the partition functions $Z_\nu(t;q)$ as $t \downarrow 0$ is derived. 
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A. A. Kvitsinskiy. Spectral functions of zeros for $q$-Bessel functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 397-414. http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a4/

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