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arXiv · hep-th/0301143

The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants

J. S. Dowker·Klaus Kirsten
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Abstract

Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which are treated both by a direct expansion method and by regularised sums. Comments on existing calculations are made. A Kaluza--Klein technique is introduced providing a determinant interpretation of the Glaisher-Kinkelin-Bendersky constants which are then generalised to arbitrary zeta-functions. This technique allows an improved treatment of sphere determinants.

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J. S. Dowker, Klaus Kirsten. 2003-01-21. The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants. https://doi.org/10.1142/s0219530505000479

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