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Combinatorics of noncommutative harmonic oscillator determinant
Abstract
We obtain an explicit evaluation of the determinants that appear in the denominators of the integrands for the iterated integrals expressing special values of the spectral zeta function of the noncommutative harmonic oscillator at integers greater than 1. The determinants in question are those of cyclic tridiagonal matrices; their explicit evaluation is carried out, in addition to the inclusion-exclusion principle, conceptionally using combinatorial arguments based on monomer-dimer systems. This explicit evaluation serves as a core component in the study of arithmetic properties such as the modularity of the special values of the spectral zeta function.
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BibTeX
@misc{wakayama2026combinatorics,
title = {{Combinatorics of noncommutative harmonic oscillator determinant}},
author = {Masato Wakayama and Wadim Zudilin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07626},
eprint = {2611.07626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07626},
}
RIS
TY - UNPB
TI - Combinatorics of noncommutative harmonic oscillator determinant
AU - Masato Wakayama
AU - Wadim Zudilin
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07626
UR - https://arxiv.org/abs/2611.07626
AB - We obtain an explicit evaluation of the determinants that appear in the denominators of the integrands for the iterated integrals expressing special values of the spectral zeta function of the noncommutative harmonic oscillator at integers greater than 1. The determinants in question are those of cyclic tridiagonal matrices; their explicit evaluation is carried out, in addition to the inclusion-exclusion principle, conceptionally using combinatorial arguments based on monomer-dimer systems. This explicit evaluation serves as a core component in the study of arithmetic properties such as the modularity of the special values of the spectral zeta function.
ER -