{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T08:47:37Z","timestamp":1771922857925,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T00:00:00Z","timestamp":1701043200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T00:00:00Z","timestamp":1701043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00493-023-00076-x","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T08:01:52Z","timestamp":1701072112000},"page":"393-416","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Group Ring Approach to Fuglede\u2019s Conjecture in Cyclic Groups"],"prefix":"10.1007","volume":"44","author":[{"given":"Tao","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,27]]},"reference":[{"issue":"8","key":"76_CR1","doi-asserted-by":"publisher","first-page":"2547","DOI":"10.1016\/j.jfa.2016.10.018","volume":"273","author":"C Aten","year":"2017","unstructured":"Aten, C., Ayachi, B., Bau, E., FitzPatrick, D., Iosevich, A., Liu, H., Lott, A., MacKinnon, I., Maimon, S., Nan, S., Pakianathan, J., Petridis, G., Rojas Mena, C., Sheikh, A., Tribone, T., Weill, J., Yu, C.: Tiling sets and spectral sets over finite fields. J. Funct. Anal. 273(8), 2547\u20132577 (2017)","journal-title":"J. Funct. Anal."},{"issue":"1","key":"76_CR2","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1006\/jabr.1998.7628","volume":"212","author":"EM Coven","year":"1999","unstructured":"Coven, E.M., Meyerowitz, A.: Tiling the integers with translates of one finite set. J. Algebra 212(1), 161\u2013174 (1999)","journal-title":"J. Algebra"},{"issue":"3","key":"76_CR3","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/s00041-013-9264-7","volume":"19","author":"DE Dutkay","year":"2013","unstructured":"Dutkay, D.E., Jorgensen, P.E.T.: On the universal tiling conjecture in dimension one. J. Fourier Anal. Appl. 19(3), 467\u2013477 (2013)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"76_CR4","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1017\/S0305004113000558","volume":"156","author":"DE Dutkay","year":"2014","unstructured":"Dutkay, D.E., Lai, C.-K.: Some reductions of the spectral set conjecture to integers. Math. Proc. Camb. Philos. Soc. 156(1), 123\u2013135 (2014)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"76_CR5","unstructured":"Fallon, T., Mayeli, A., Villano, D.: The fuglede\u2019s conjecture holds in $$\\mathbb{F} _{p}^{3}$$ for $$p=5,7$$. Proc. Am. Math. Soc. To appear"},{"issue":"12","key":"76_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2022.109472","volume":"282","author":"T Fallon","year":"2022","unstructured":"Fallon, T., Kiss, G., Somlai, G.: Spectral sets and tiles in $$\\mathbb{Z} _{p}^{2}\\times \\mathbb{Z} _{q}^{2}$$. J. Funct. Anal. 282(12), 109472 (2022)","journal-title":"J. Funct. Anal."},{"issue":"12","key":"76_CR7","doi-asserted-by":"publisher","first-page":"3628","DOI":"10.1016\/j.jfa.2016.08.021","volume":"271","author":"A Fan","year":"2016","unstructured":"Fan, A., Fan, S., Shi, R.: Compact open spectral sets in $$\\mathbb{Q} _p$$. J. Funct. Anal. 271(12), 3628\u20133661 (2016)","journal-title":"J. Funct. Anal."},{"issue":"1\u20132","key":"76_CR8","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s00208-019-01867-8","volume":"375","author":"A Fan","year":"2019","unstructured":"Fan, A., Fan, S., Liao, L., Shi, R.: Fuglede\u2019s conjecture holds in $$\\mathbb{Q} _p$$. Math. Ann. 375(1\u20132), 315\u2013341 (2019)","journal-title":"Math. Ann."},{"issue":"5","key":"76_CR9","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s00041-005-5069-7","volume":"12","author":"B Farkas","year":"2006","unstructured":"Farkas, B., Matolcsi, M., M\u00f3ra, P.: On Fuglede\u2019s conjecture and the existence of universal spectra. J. Fourier Anal. Appl. 12(5), 483\u2013494 (2006)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"76_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2019.04.026","volume":"343","author":"SJ Ferguson","year":"2020","unstructured":"Ferguson, S.J., Sothanaphan, N.: Fuglede\u2019s conjecture fails in 4 dimensions over odd prime fields. Discret. Math. 343(1), 111507, 7 (2020)","journal-title":"Discret. Math."},{"key":"76_CR11","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0022-1236(74)90072-X","volume":"16","author":"B Fuglede","year":"1974","unstructured":"Fuglede, B.: Commuting self-adjoint partial differential operators and a group theoretic problem. J. Funct. Anal. 16, 101\u2013121 (1974)","journal-title":"J. Funct. Anal."},{"issue":"6","key":"76_CR12","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.2140\/apde.2017.10.1497","volume":"10","author":"R Greenfeld","year":"2017","unstructured":"Greenfeld, R., Lev, N.: Fuglede\u2019s spectral set conjecture for convex polytopes. Anal. PDE 10(6), 1497\u20131538 (2017)","journal-title":"Anal. PDE"},{"issue":"5\u20136","key":"76_CR13","doi-asserted-by":"publisher","first-page":"559","DOI":"10.4310\/MRL.2003.v10.n5.a1","volume":"10","author":"A Iosevich","year":"2003","unstructured":"Iosevich, A., Katz, N., Tao, T.: The Fuglede spectral conjecture holds for convex planar domains. Math. Res. Lett. 10(5\u20136), 559\u2013569 (2003)","journal-title":"Math. Res. Lett."},{"issue":"4","key":"76_CR14","doi-asserted-by":"publisher","first-page":"757","DOI":"10.2140\/apde.2017.10.757","volume":"10","author":"A Iosevich","year":"2017","unstructured":"Iosevich, A., Mayeli, A., Pakianathan, J.: The Fuglede conjecture holds in $$\\mathbb{Z} _p\\times \\mathbb{Z} _p$$. Anal. PDE 10(4), 757\u2013764 (2017)","journal-title":"Anal. PDE"},{"issue":"10","key":"76_CR15","doi-asserted-by":"publisher","first-page":"4181","DOI":"10.1090\/proc\/15541","volume":"149","author":"G Kiss","year":"2021","unstructured":"Kiss, G., Somlai, G.: Fuglede\u2019s conjecture holds on $$\\mathbb{Z} _{p}^{2}\\times \\mathbb{Z} _{q}$$. Proc. Am. Math. Soc. 149(10), 4181\u20134188 (2021)","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"76_CR16","doi-asserted-by":"publisher","first-page":"765","DOI":"10.2140\/apde.2020.13.765","volume":"13","author":"G Kiss","year":"2020","unstructured":"Kiss, G., Malikiosis, R.D., Somlai, G., Vizer, M.: On the discrete Fuglede and Pompeiu problems. Anal. PDE 13(3), 765\u2013788 (2020)","journal-title":"Anal. PDE"},{"key":"76_CR17","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00041-022-09972-0","volume":"28","author":"G Kiss","year":"2022","unstructured":"Kiss, G., Malikiosis, R.D., Somlai, G., Vizer, M.: Fuglede\u2019s conjecture holds for cyclic groups of order $$pqrs$$. J. Fourier Anal. Appl. 28, 79 (2022)","journal-title":"J. Fourier Anal. Appl."},{"key":"76_CR18","unstructured":"Kolountzakis, M.N., Matolcsi, M.: Complex Hadamard matrices and the spectral set conjecture. Collect. Math. (Vol. Extra), 281\u2013291 (2006)"},{"issue":"3","key":"76_CR19","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1515\/FORUM.2006.026","volume":"18","author":"MN Kolountzakis","year":"2006","unstructured":"Kolountzakis, M.N., Matolcsi, M.: Tiles with no spectra. Forum Math. 18(3), 519\u2013528 (2006)","journal-title":"Forum Math."},{"issue":"3","key":"76_CR20","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1112\/S0024610702003149","volume":"65","author":"I \u0141aba","year":"2002","unstructured":"\u0141aba, I.: The spectral set conjecture and multiplicative properties of roots of polynomials. J. Lond. Math. Soc. (2) 65(3), 661\u2013671 (2002)","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"76_CR21","unstructured":"\u0141aba, I., Londner, I.: Splitting for integer tilings and the Coven-Meyerowitz tiling conditions. arXiv:2207.11809"},{"key":"76_CR22","doi-asserted-by":"publisher","first-page":"e8 1","DOI":"10.1017\/fmp.2022.3","volume":"10","author":"I \u0141aba","year":"2022","unstructured":"\u0141aba, I., Londner, I.: Combinatorial and harmonic-analytic methods for integer tilings. Forum Math. Pi 10, e8 1-46 (2022)","journal-title":"Forum Math. Pi"},{"key":"76_CR23","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s00222-022-01169-y","volume":"232","author":"I \u0141aba","year":"2023","unstructured":"\u0141aba, I., Londner, I.: The Coven-Meyerowitz tiling conditions for 3 odd prime factors. Invent. Math. 232, 365\u2013470 (2023)","journal-title":"Invent. Math."},{"issue":"2","key":"76_CR24","doi-asserted-by":"publisher","first-page":"385","DOI":"10.4310\/ACTA.2022.v228.n2.a3","volume":"228","author":"N Lev","year":"2022","unstructured":"Lev, N., Matolcsi, M.: The Fuglede conjecture for convex domains is true in all dimensions. Acta Math. 228(2), 385\u2013420 (2022)","journal-title":"Acta Math."},{"key":"76_CR25","doi-asserted-by":"publisher","first-page":"e23 1","DOI":"10.1017\/fms.2022.14","volume":"10","author":"RD Malikiosis","year":"2022","unstructured":"Malikiosis, R.D.: On the structure of spectral and tiling subsets of cyclic groups. Forum Math. Sigma 10, e23 1-42 (2022)","journal-title":"Forum Math. Sigma"},{"key":"76_CR26","doi-asserted-by":"crossref","unstructured":"Malikiosis, R.D., Kolountzakis, M.N.: Fuglede\u2019s conjecture on cyclic groups of order $$p^n q$$. Discret. Anal., Paper No. 12, 16 (2017)","DOI":"10.19086\/da.2071"},{"issue":"10","key":"76_CR27","doi-asserted-by":"publisher","first-page":"3021","DOI":"10.1090\/S0002-9939-05-07874-3","volume":"133","author":"M Matolcsi","year":"2005","unstructured":"Matolcsi, M.: Fuglede\u2019s conjecture fails in dimension 4. Proc. Am. Math. Soc. 133(10), 3021\u20133026 (2005)","journal-title":"Proc. Am. Math. Soc."},{"key":"76_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0094449","volume-title":"Finite Geometry and Character Theory","author":"A Pott","year":"1995","unstructured":"Pott, A.: Finite Geometry and Character Theory, vol. 1601. Springer, Berlin (1995)"},{"key":"76_CR29","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/b84213","volume-title":"Characters and Cyclotomic Fields in Finite Geometry","author":"B Schmidt","year":"2002","unstructured":"Schmidt, B.: Characters and Cyclotomic Fields in Finite Geometry. Lecture Notes in Mathematics, vol. 1797. Springer, Berlin (2002)"},{"key":"76_CR30","unstructured":"Shi, R.: Fuglede\u2019s conjecture holds on cyclic groups $$\\mathbb{Z}_{pqr}$$. Discret. Anal., Paper No. 14, 14 (2019)"},{"issue":"3","key":"76_CR31","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1112\/jlms.12346","volume":"102","author":"R Shi","year":"2020","unstructured":"Shi, R.: Equi-distributed property and spectral set conjecture on $$\\mathbb{Z} _{p^2} \\times \\mathbb{Z} _p$$. J. Lond. Math. Soc. (2) 102(3), 1030\u20131046 (2020)","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"76_CR32","unstructured":"Somlai, G.: Spectral sets in $$\\mathbb{Z}_{p^{2}qr}$$ tile. Discret. Anal., Paper No. 5, 10, (2023)"},{"key":"76_CR33","series-title":"Lecture Notes in Pure and Applied Mathematics","doi-asserted-by":"publisher","DOI":"10.1201\/9781420090475","volume-title":"Factoring Groups into Subsets","author":"S Szab\u00f3","year":"2009","unstructured":"Szab\u00f3, S., Sands, A.D.: Factoring Groups into Subsets. Lecture Notes in Pure and Applied Mathematics, vol. 257. CRC Press, Boca Raton, FL (2009)"},{"key":"76_CR34","unstructured":"Tao, T.: Some notes on the coven-meyerowitz conjecture. https:\/\/terrytao.wordpress.com\/2011\/11\/19\/some-notes-on-the-coven-meyerowitz-conjecture\/"},{"issue":"2\u20133","key":"76_CR35","doi-asserted-by":"publisher","first-page":"251","DOI":"10.4310\/MRL.2004.v11.n2.a8","volume":"11","author":"T Tao","year":"2004","unstructured":"Tao, T.: Fuglede\u2019s conjecture is false in 5 and higher dimensions. Math. Res. Lett. 11(2\u20133), 251\u2013258 (2004)","journal-title":"Math. Res. Lett."},{"key":"76_CR36","doi-asserted-by":"crossref","unstructured":"Zhang, T.: Fuglede\u2019s conjecture holds in $$\\mathbb{Z} _{p}\\times \\mathbb{Z} _{p^n}$$. SIAM J. Discret. Math. 37(2), 1180\u20131197 (2023)","DOI":"10.1137\/22M1493598"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-023-00076-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-023-00076-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-023-00076-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T22:01:52Z","timestamp":1711058512000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-023-00076-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,27]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["76"],"URL":"https:\/\/doi.org\/10.1007\/s00493-023-00076-x","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,27]]},"assertion":[{"value":"16 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}