{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:56:38Z","timestamp":1753872998523,"version":"3.41.2"},"reference-count":43,"publisher":"AIP Publishing","issue":"2","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2011,2,1]]},"abstract":"<jats:p>The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless D-dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.<\/jats:p>","DOI":"10.1063\/1.3545705","type":"journal-article","created":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T23:11:02Z","timestamp":1296774662000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Zeta determinant for Laplace operators on Riemann caps"],"prefix":"10.1063","volume":"52","author":[{"given":"Antonino","family":"Flachi","sequence":"first","affiliation":[{"name":"Kyoto University 1 Yukawa Institute for Theoretical Physics, , Kyoto, Japan"}]},{"given":"Guglielmo","family":"Fucci","sequence":"additional","affiliation":[{"name":"Baylor University 2 Department of Mathematics, , Waco, Texas 76798, USA"}]}],"member":"317","published-online":{"date-parts":[[2011,2,3]]},"reference":[{"key":"2023062722005057400_c1","doi-asserted-by":"publisher","first-page":"3224","DOI":"10.1103\/PhysRevD.13.3224","volume":"13","year":"1976","journal-title":"Phys. Rev. D"},{"key":"2023062722005057400_c2","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF01626516","volume":"55","year":"1977","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c3","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0001-8708(71)90045-4","volume":"7","year":"1971","journal-title":"Adv. Math."},{"volume-title":"Quantum Field Theory in Curved Spacetime","year":"2009","key":"2023062722005057400_c4"},{"key":"2023062722005057400_c5","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/BF02101749","volume":"162","year":"1994","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c6","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/0550-3213(93)90223-C","volume":"395","year":"1993","journal-title":"Nucl. Phys. B"},{"key":"2023062722005057400_c7","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1216\/rmjm\/1181075478","volume":"33","year":"2003","journal-title":"Rocky Mt. J. Math."},{"key":"2023062722005057400_c8","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/BF02103720","volume":"179","year":"1996","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0370-1573(90)90120-Q","volume":"196","year":"1990","journal-title":"Phys. Rep."},{"key":"2023062722005057400_c10","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/BF02517895","volume":"182","year":"1996","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c11","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/BF01391828","volume":"88","year":"1987","journal-title":"Invent. Math."},{"key":"2023062722005057400_c12","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1007\/s00220-007-0229-z","volume":"273","year":"2007","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c13","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0003-4916(92)90347-O","volume":"219","year":"1992","journal-title":"Ann. Phys."},{"key":"2023062722005057400_c14","doi-asserted-by":"publisher","first-page":"124011","DOI":"10.1103\/PhysRevD.70.124011","volume":"70","year":"2004","journal-title":"Phys. Rev. D"},{"volume-title":"Proceedings of the Fourteenth Workshop on General Relativity and Gravitation in Japan","year":"2004","first-page":"239","key":"2023062722005057400_c15"},{"volume-title":"Asymptotics and Special Functions","year":"1997","author":"Peters","key":"2023062722005057400_c16"},{"key":"2023062722005057400_c17","first-page":"575","volume":"18","year":"1983","journal-title":"J. Diff. Geom."},{"key":"2023062722005057400_c18","doi-asserted-by":"publisher","first-page":"2320","DOI":"10.1063\/1.1559414","volume":"44","year":"2003","journal-title":"J. Math. Phys."},{"key":"2023062722005057400_c19","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1098\/rsta.1957.0008","volume":"249","year":"1957","journal-title":"Philos. Trans. R. Soc. London"},{"volume-title":"Invariance Theory the Heat Equation and the Atiyah-Singer Index Theorem","year":"1995","key":"2023062722005057400_c20"},{"key":"2023062722005057400_c21","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/BF01456084","volume":"268","year":"1984","journal-title":"Math. Ann."},{"key":"2023062722005057400_c22","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/0022-1236(87)90073-5","volume":"73","year":"1987","journal-title":"J. Funct. Anal."},{"volume-title":"Spectral Functions in Mathematics and Physics","year":"2001","key":"2023062722005057400_c23"},{"key":"2023062722005057400_c24","doi-asserted-by":"publisher","first-page":"083516","DOI":"10.1063\/1.2259580","volume":"47","year":"2006","journal-title":"J. Math. Phys."},{"key":"2023062722005057400_c25","doi-asserted-by":"publisher","first-page":"024004","DOI":"10.1103\/PhysRevD.69.024004","volume":"69","year":"2004","journal-title":"Phys. Rev. D"},{"key":"2023062722005057400_c26","doi-asserted-by":"publisher","first-page":"043506","DOI":"10.1063\/1.2189194","volume":"47","year":"2006","journal-title":"J. Math. Phys."},{"volume-title":"Ten Physical Applications of the Spectral Zeta Function","year":"1995","key":"2023062722005057400_c27"},{"key":"2023062722005057400_c28","doi-asserted-by":"publisher","first-page":"2483","DOI":"10.1088\/0305-4470\/27\/7\/025","volume":"26","year":"1994","journal-title":"J. Phys. A"},{"volume-title":"Table of Integrals, Series and Products","year":"2007","author":"Jeffrey","key":"2023062722005057400_c29"},{"key":"2023062722005057400_c30","doi-asserted-by":"publisher","first-page":"365204","DOI":"10.1088\/1751-8113\/43\/36\/365204","volume":"43","year":"2010","journal-title":"J. Phys. A: Math. Theor."},{"volume-title":"Euclidean Quantum Gravity on Manifolds with Boundaries","year":"1997","key":"2023062722005057400_c31"},{"key":"2023062722005057400_c32","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.physrep.2003.09.002","volume":"388","year":"2003","journal-title":"Phys. Rep."},{"key":"2023062722005057400_c33","doi-asserted-by":"publisher","first-page":"L27","DOI":"10.1088\/0264-9381\/9\/2\/002","volume":"9","year":"1992","journal-title":"Class. Quantum Grav."},{"key":"2023062722005057400_c34","first-page":"374","volume":"19","year":"1904","journal-title":"Trans. Cambridge Philos. Soc."},{"key":"2023062722005057400_c35","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1142\/S0219530505000479","volume":"3","year":"2005","journal-title":"Anal. Appl."},{"key":"2023062722005057400_c36","doi-asserted-by":"publisher","first-page":"102301","DOI":"10.1063\/1.3231787","volume":"50","year":"2009","journal-title":"J. Math. Phys."},{"key":"2023062722005057400_c37","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/S0377-0427(98)00193-9","volume":"100","year":"1998","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"2023062722005057400_c38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.chemphys.2008.02.044","volume":"60","year":"2008","journal-title":"J. High Energy Phys."},{"issue":"3","key":"2023062722005057400_c39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/1126-6708\/2009\/03\/124","volume":"124","year":"2009","journal-title":"J. High Energy Phys."},{"key":"2023062722005057400_c40","doi-asserted-by":"publisher","first-page":"084018","DOI":"10.1103\/PhysRevD.78.084018","volume":"78","year":"2008","journal-title":"Phys. Rev. D"},{"key":"2023062722005057400_c41","doi-asserted-by":"publisher","first-page":"084031","DOI":"10.1103\/PhysRevD.76.084031","volume":"76","year":"2007","journal-title":"Phys. Rev. D"},{"key":"2023062722005057400_c42","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/s002200050371","volume":"194","year":"1998","journal-title":"Commun. Math. Phys."},{"key":"2023062722005057400_c43","doi-asserted-by":"publisher","first-page":"7430","DOI":"10.1103\/PhysRevD.57.7430","volume":"57","year":"1998","journal-title":"Phys. Rev. D"}],"container-title":["Journal of Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/doi\/10.1063\/1.3545705\/15655119\/023503_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/doi\/10.1063\/1.3545705\/15655119\/023503_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T22:01:00Z","timestamp":1687903260000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jmp\/article\/52\/2\/023503\/232748\/Zeta-determinant-for-Laplace-operators-on-Riemann"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,1]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,2,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.3545705","relation":{},"ISSN":["0022-2488","1089-7658"],"issn-type":[{"type":"print","value":"0022-2488"},{"type":"electronic","value":"1089-7658"}],"subject":[],"published-other":{"date-parts":[[2011,2]]},"published":{"date-parts":[[2011,2,1]]},"article-number":"023503"}}