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Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems (2303.10004v2)
Published 17 Mar 2023 in math.CO, math.NT, and math.SP
Abstract: In this paper, we apply the combinatorial results on counting permutations with fixed pinnacle and vale sets to evaluate the special values of the spectral zeta functions of Sturm-Liouville differential operators. As applications, we get a combinatorial formula for the special values of spectral zeta functions and give a new explicit formula for Bernoulli numbers.
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