Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces
For a nonnegative integer, we consider the -Laplacian Δₙ acting on the space of -differentials on a confinite Riemann surface X which has ramification points. The trace formula for the resolvent kernel is developed along the line à la Selberg. Using the trace formula, we compute the regularized det...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211444 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces. Lee-Peng Teo. SIGMA 17 (2021), 083, 40 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862645151282757632 |
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| author | Teo, Lee-Peng |
| author_facet | Teo, Lee-Peng |
| citation_txt | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces. Lee-Peng Teo. SIGMA 17 (2021), 083, 40 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For a nonnegative integer, we consider the -Laplacian Δₙ acting on the space of -differentials on a confinite Riemann surface X which has ramification points. The trace formula for the resolvent kernel is developed along the line à la Selberg. Using the trace formula, we compute the regularized determinant of Δₙ + ( + 2 − 1), from which we deduce the regularized determinant of Δₙ, denoted by det′Δₙ. Taking into account the contribution from the absolutely continuous spectrum, det′Δₙ is equal to a constant Cₙ times () when ≥ 2. Here () is the Selberg zeta function of . When = 0 or = 1, () is replaced by the leading coefficient of the Taylor expansion of () around = 0 and = 1, respectively. The constants Cn are calculated explicitly. They depend on the genus, the number of cusps, as well as the ramification indices, but are independent of the moduli parameters.
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| first_indexed | 2026-03-15T10:21:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211444 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T10:21:32Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Teo, Lee-Peng 2026-01-02T08:35:30Z 2021 Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces. Lee-Peng Teo. SIGMA 17 (2021), 083, 40 pages 1815-0659 2020 Mathematics Subject Classification: 14H15; 11F72; 11M36 arXiv:2104.00895 https://nasplib.isofts.kiev.ua/handle/123456789/211444 https://doi.org/10.3842/SIGMA.2021.083 For a nonnegative integer, we consider the -Laplacian Δₙ acting on the space of -differentials on a confinite Riemann surface X which has ramification points. The trace formula for the resolvent kernel is developed along the line à la Selberg. Using the trace formula, we compute the regularized determinant of Δₙ + ( + 2 − 1), from which we deduce the regularized determinant of Δₙ, denoted by det′Δₙ. Taking into account the contribution from the absolutely continuous spectrum, det′Δₙ is equal to a constant Cₙ times () when ≥ 2. Here () is the Selberg zeta function of . When = 0 or = 1, () is replaced by the leading coefficient of the Taylor expansion of () around = 0 and = 1, respectively. The constants Cn are calculated explicitly. They depend on the genus, the number of cusps, as well as the ramification indices, but are independent of the moduli parameters. This research is supported by the Ministry of Higher Education Malaysia through the Fundamental Research Grant Scheme (FRGS) FRGS/1/2018/STG06/XMU/01/1. We would like to thank L. Takhtajan and J. Friedman, who have given helpful comments and suggestions. We would also like to thank the referees for carefully reviewing the paper and providing valuable comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces Article published earlier |
| spellingShingle | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces Teo, Lee-Peng |
| title | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces |
| title_full | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces |
| title_fullStr | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces |
| title_full_unstemmed | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces |
| title_short | Resolvent Trace Formula and Determinants of Laplacians on Orbifold Riemann Surfaces |
| title_sort | resolvent trace formula and determinants of laplacians on orbifold riemann surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211444 |
| work_keys_str_mv | AT teoleepeng resolventtraceformulaanddeterminantsoflaplaciansonorbifoldriemannsurfaces |