{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T04:12:20Z","timestamp":1742271140171,"version":"3.40.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T00:00:00Z","timestamp":1702080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T00:00:00Z","timestamp":1702080000000},"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":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s00454-023-00615-9","type":"journal-article","created":{"date-parts":[[2023,12,9]],"date-time":"2023-12-09T19:01:31Z","timestamp":1702148491000},"page":"850-858","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved Estimates on the Number of Unit Perimeter Triangles"],"prefix":"10.1007","volume":"73","author":[{"given":"Ritesh","family":"Goenka","sequence":"first","affiliation":[]},{"given":"Kenneth","family":"Moore","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5819-0634","authenticated-orcid":false,"given":"Ethan Patrick","family":"White","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,9]]},"reference":[{"issue":"1","key":"615_CR1","first-page":"87","volume":"2","author":"I Boreico","year":"2008","unstructured":"Boreico, I.: My favorite problem: linear independence of radicals. Harvard College Math Review 2(1), 87\u201393 (2008)","journal-title":"Harvard College Math Review"},{"key":"615_CR2","volume-title":"Pi and the AGM","author":"JM Borwein","year":"1987","unstructured":"Borwein, J.M., Borwein, P.B.: Pi and the AGM. Wiley, New York (1987)"},{"key":"615_CR3","volume-title":"Research Problems in Discrete Geometry","author":"P Brass","year":"2005","unstructured":"Brass, P., Moser, W., Pach, J.: Research Problems in Discrete Geometry. Springer, New York (2005)"},{"issue":"1","key":"615_CR4","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1142\/S1793042109002018","volume":"5","author":"R Carr","year":"2009","unstructured":"Carr, R., O\u2019Sullivan, C.: On the linear independence of roots. Int. J. Number Theory 5(1), 161\u2013171 (2009)","journal-title":"Int. J. Number Theory"},{"key":"615_CR5","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1080\/00029890.1946.11991674","volume":"53","author":"P Erd\u0151s","year":"1946","unstructured":"Erd\u0151s, P.: On sets of distances of $$n$$ points. Am. Math. Monthly 53, 248\u2013250 (1946)","journal-title":"Am. Math. Monthly"},{"key":"615_CR6","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/0097-3165(71)90028-8","volume":"10","author":"P Erd\u0151s","year":"1971","unstructured":"Erd\u0151s, P., Purdy, G.: Some extremal problems in geometry. J. Comb. Theory Ser. A 10, 246\u2013252 (1971)","journal-title":"J. Comb. Theory Ser. A"},{"key":"615_CR7","series-title":"Graduate Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/017","volume-title":"Topics in Classical Automorphic Forms","author":"H Iwaniec","year":"1997","unstructured":"Iwaniec, H.: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics, vol. 17. American Mathematical Society, Providence (1997)"},{"issue":"4","key":"615_CR8","doi-asserted-by":"publisher","first-page":"485","DOI":"10.4153\/CMB-1983-078-5","volume":"26","author":"J-L Nicolas","year":"1983","unstructured":"Nicolas, J.-L., Robin, G.: Majorations explicites pour le nombre de diviseurs de $$N$$. Can. Math. Bull. 26(4), 485\u2013492 (1983)","journal-title":"Can. Math. Bull."},{"key":"615_CR9","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1090\/S0002-9904-1941-07496-3","volume":"47","author":"CD Olds","year":"1941","unstructured":"Olds, C.D.: On the representations, $$N_3(n^2)$$. Bull. Am. Math. Soc. 47, 499\u2013503 (1941)","journal-title":"Bull. Am. Math. Soc."},{"key":"615_CR10","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/0097-3165(92)90094-B","volume":"59","author":"J Pach","year":"1992","unstructured":"Pach, J., Sharir, M.: Repeated angles in the plane and related problems. J. Comb. Theory Ser. A 59, 12\u201322 (1992)","journal-title":"J. Comb. Theory Ser. A"},{"key":"615_CR11","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1017\/S0963548397003192","volume":"7","author":"J Pach","year":"1998","unstructured":"Pach, J., Sharir, M.: On the number of incidences between points and curves. Comb. Probab. Comput. 7, 121\u2013127 (1998)","journal-title":"Comb. Probab. Comput."},{"key":"615_CR12","series-title":"Contemporary Mathematics","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1090\/conm\/342\/06151","volume-title":"Towards a Theory of Geometric Graphs","author":"J Pach","year":"2004","unstructured":"Pach, J., Sharir, M.: Geometric incidences. In: Towards a Theory of Geometric Graphs. Contemporary Mathematics, vol. 342, pp. 185\u2013223. American Mathematical Society, Providence (2004)"},{"key":"615_CR13","first-page":"311","volume":"19","author":"G Pick","year":"1899","unstructured":"Pick, G.: Geometrisches zur Zahlenlehre. Sitzungber. Lotos (Prague) 19, 311\u2013319 (1899)","journal-title":"Sitzungber. Lotos (Prague)"},{"key":"615_CR14","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.1007\/s00493-016-3440-8","volume":"37","author":"OE Raz","year":"2017","unstructured":"Raz, O.E., Sharir, M.: The number of unit-area triangles in the plane: theme and variations. Combinatorica 37, 1221\u20131240 (2017)","journal-title":"Combinatorica"},{"key":"615_CR15","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.comgeo.2016.12.002","volume":"62","author":"OE Raz","year":"2017","unstructured":"Raz, O.E., Sharir, M., Shkredov, I.D.: On the number of unit-area triangles spanned by convex grids in the plane. Comput. Geom. 62, 25\u201333 (2017)","journal-title":"Comput. Geom."},{"key":"615_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jcta.2017.02.006","volume":"150","author":"M Sharir","year":"2017","unstructured":"Sharir, M., Zahl, J.: Cutting algebraic curves into pseudo-segments and applications. J. Comb. Theory Ser. A 150, 1\u201335 (2017)","journal-title":"J. Comb. Theory Ser. A"},{"key":"615_CR17","unstructured":"Shelestunova, V.: Upper bounds for the number of integral points on quadratic curves and surfaces, Ph. D. thesis, University of Waterloo, Ontario, Canada (2010)"},{"key":"615_CR18","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1080\/00029890.2001.11919751","volume":"108","author":"P Yiu","year":"2001","unstructured":"Yiu, P.: Heronian triangles are lattice triangles. Am. Math. Mon. 108, 261\u2013263 (2001)","journal-title":"Am. Math. Mon."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00615-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-023-00615-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00615-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T14:57:58Z","timestamp":1742223478000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-023-00615-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,9]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["615"],"URL":"https:\/\/doi.org\/10.1007\/s00454-023-00615-9","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2023,12,9]]},"assertion":[{"value":"1 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}