On Dirichlet eigenvalues of regular polygons
We prove that the first Dirichlet eigenvalue of a regular N-gon of area π has an asymptotic expansion of the form λ1(1+∑n≥3Cn(λ1)Nn) as N→∞, where λ1 is the first Dirichlet eigenvalue of the unit disk and Cn are polynomials whose coefficients belong to the space of multiple zeta values of weight n a...
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Published in | Journal of mathematical analysis and applications Vol. 538; no. 2; p. 128460 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
15.10.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We prove that the first Dirichlet eigenvalue of a regular N-gon of area π has an asymptotic expansion of the form λ1(1+∑n≥3Cn(λ1)Nn) as N→∞, where λ1 is the first Dirichlet eigenvalue of the unit disk and Cn are polynomials whose coefficients belong to the space of multiple zeta values of weight n and conjecture that their coefficients lie in the space of single-valued multiple zeta values. We also explicitly compute these polynomials for all n≤14. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2024.128460 |