{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T01:48:09Z","timestamp":1743040089696,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":33,"publisher":"Springer New York","isbn-type":[{"type":"print","value":"9781461472575"},{"type":"electronic","value":"9781461472582"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-1-4614-7258-2_14","type":"book-chapter","created":{"date-parts":[[2013,8,1]],"date-time":"2013-08-01T18:28:13Z","timestamp":1375381693000},"page":"207-220","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Landau\u2019s Function g(n)"],"prefix":"10.1007","author":[{"given":"Jean-Louis","family":"Nicolas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,5,20]]},"reference":[{"key":"14_CR1","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1090\/S0002-9947-1944-0011087-2","volume":"56","author":"L Alaoglu","year":"1944","unstructured":"L. Alaoglu, P. Erd\u0151s, \u201cOn highly composite and similar numbers\u201d, Trans. Amer. Math. Soc. 56, 1944, 448\u2013469.","journal-title":"Trans. Amer. Math. Soc."},{"key":"14_CR2","doi-asserted-by":"publisher","first-page":"625","DOI":"10.5802\/jtnb.644","volume":"20","author":"M Del\u00e9glise","year":"2008","unstructured":"M. Del\u00e9glise, J.-L. Nicolas, P. Zimmermann, \u201cLandau\u2019s function for one million billions\u201d, J. de Th\u00e9orie des Nombres de Bordeaux, 20, 2008, 625\u2013671.","journal-title":"J. de Th\u00e9orie des Nombres de Bordeaux"},{"key":"14_CR3","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s11139-011-9293-2","volume":"27","author":"M Del\u00e9glise","year":"2012","unstructured":"M. Del\u00e9glise, J.-L. Nicolas, \u201cLe plus grand facteur premier de la fonction de Landau\u201d, Ramanujan J., 27, 2012, 109\u2013145.","journal-title":"Ramanujan J."},{"key":"14_CR4","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1112\/jlms\/19.75_Part_3.130","volume":"19","author":"P Erd\u0151s","year":"1944","unstructured":"P. Erd\u0151s, \u201cOn highly composited numbers\u201d, J. London Math. Soc., 19, 1944, 130\u2013133.","journal-title":"J. London Math. Soc."},{"key":"14_CR5","doi-asserted-by":"crossref","unstructured":"P. Erd\u0151s, \u201cRamanujan and I\u201d, Number Theory, Madras 1987, Editor : K. Alladi, Lecture Notes in Mathematics n\n                  o\n                 1395, Springer-Verlag, 1989.","DOI":"10.1007\/BFb0086396"},{"key":"14_CR6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.24033\/bsmf.1793","volume":"103","author":"P Erd\u0151s","year":"1975","unstructured":"P. Erd\u0151s, J.-L. Nicolas, \u201cR\u00e9partition des nombres superabondants\u201d, Bull. Soc. Math. France, 103, 1975, 65\u201390.","journal-title":"Bull. Soc. Math. France"},{"key":"#cr-split#-14_CR7.1","doi-asserted-by":"crossref","unstructured":"P. Erd\u0151s, P. Turan, \"On some problems of a statistical group theory\", I to VII, Zeitschr. fur Wahrschenlichkeitstheorie und verw. Gebiete, 4, 1965, 175-186","DOI":"10.1007\/BF00536750"},{"key":"#cr-split#-14_CR7.2","doi-asserted-by":"crossref","unstructured":"Acta Math. Hung., 18, 1967, 151-163","DOI":"10.1007\/BF02020968"},{"key":"#cr-split#-14_CR7.3","doi-asserted-by":"crossref","unstructured":"Acta Math. Hung., 18, 1967, 309-320","DOI":"10.1017\/S0001925900004303"},{"key":"#cr-split#-14_CR7.4","doi-asserted-by":"crossref","unstructured":"Acta Math. Hung., 19, 1968, 413-435","DOI":"10.1007\/BF01894517"},{"key":"#cr-split#-14_CR7.5","doi-asserted-by":"crossref","unstructured":"Periodica Math. Hung., 1, 1971, 5-13","DOI":"10.1007\/BF02095631"},{"key":"#cr-split#-14_CR7.6","unstructured":"J. Indian Math. Soc., 34, 1970, 175-192"},{"key":"#cr-split#-14_CR7.7","doi-asserted-by":"crossref","unstructured":"Periodica Math. Hung., 2, 1972, 149-163.","DOI":"10.1007\/BF02018658"},{"key":"14_CR8","first-page":"407","volume":"64","author":"J Grantham","year":"1995","unstructured":"J. Grantham, \u201cThe largest prime dividing the maximal order of an element of S\n                \n                  n\n                \u201d, Math. Comp., 64, 1995, 407\u2013410.","journal-title":"Math. Comp."},{"key":"14_CR9","unstructured":"E. Landau, \u201cUber die Maximalordung der Permutation gegebenen Grades\u201d, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1, 2nd edition, Chelsea, New-York, 1953, 222\u2013229."},{"key":"14_CR10","doi-asserted-by":"publisher","first-page":"269","DOI":"10.5802\/afst.612","volume":"6","author":"J P Massias","year":"1984","unstructured":"J. P. Massias, \u201cMajoration explicite de l\u2019ordre maximum d\u2019un \u00e9l\u00e9ment du groupe sym\u00e9trique\u201d, Ann. Fac. Sci. Toulouse Math., 6, 1984, 269\u2013281.","journal-title":"Ann. Fac. Sci. Toulouse Math."},{"key":"14_CR11","doi-asserted-by":"crossref","first-page":"221","DOI":"10.4064\/aa-50-3-221-242","volume":"50","author":"J P Massias","year":"1988","unstructured":"J. P. Massias, J.-L. Nicolas, G. Robin, \u201cEvaluation asymptotique de l\u2019ordre maximum d\u2019un \u00e9l\u00e9ment du groupe sym\u00e9trique\u201d, Acta Arithmetica, 50, 1988, 221\u2013242.","journal-title":"Acta Arithmetica"},{"key":"14_CR12","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1090\/S0025-5718-1989-0979940-4","volume":"53","author":"J P Massias","year":"1989","unstructured":"J. P. Massias, J.-L. Nicolas, G. Robin, \u201cEffective bounds for the Maximal Order of an Element in the Symmetric Group\u201d, Math. Comp., 53, 1989, 665\u2013678.","journal-title":"Math. Comp."},{"key":"14_CR13","doi-asserted-by":"publisher","first-page":"497","DOI":"10.2307\/2322839","volume":"94","author":"W Miller","year":"1987","unstructured":"W. Miller, \u201cThe Maximum Order of an Element of a Finite Symmetric Group\u201d, Amer. Math. Monthly, 94, 1987, 497\u2013506.","journal-title":"Amer. Math. Monthly"},{"key":"14_CR14","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1112\/S0025579300004708","volume":"20","author":"H L Montgomery","year":"1973","unstructured":"H. L. Montgomery, R. C. Vaughan, \u201cThe large sieve\u201d, Mathematika, 20, 1973, 119\u2013134.","journal-title":"Mathematika"},{"key":"14_CR15","doi-asserted-by":"crossref","first-page":"315","DOI":"10.4064\/aa-14-3-315-332","volume":"14","author":"J.-L. Nicolas","year":"1968","unstructured":"J.-L. Nicolas, \u201cSur l\u2019ordre maximum d\u2019un \u00e9l\u00e9ment dans le groupe S\n                \n                  n\n                 des permutations\u201d, Acta Arithmetica, 14, 1968, 315\u2013332.","journal-title":"Acta Arithmetica"},{"key":"14_CR16","doi-asserted-by":"crossref","first-page":"129","DOI":"10.24033\/bsmf.1676","volume":"97","author":"J.-L. Nicolas","year":"1969","unstructured":"J.-L. Nicolas, \u201cOrdre maximum d\u2019un \u00e9l\u00e9ment du groupe de permutations et highly composite numbers\u201d, Bull. Soc. Math. France, 97, 1969, 129\u2013191.","journal-title":"Bull. Soc. Math. France"},{"key":"14_CR17","unstructured":"J.-L. Nicolas, \u201cOrdre maximal d\u2019un \u00e9l\u00e9ment d\u2019un groupe de permutations\u201d, C.R. Acad. Sci. Paris, 270, 1970, 1473\u20131476."},{"key":"14_CR18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.4064\/aa-34-4-379-390","volume":"34","author":"J.-L. Nicolas","year":"1979","unstructured":"J.-L. Nicolas, \u201cR\u00e9partition des nombres largement compos\u00e9s\u201d, Acta Arithmetica, 34, 1979, 379\u2013390.","journal-title":"Acta Arithmetica"},{"key":"#cr-split#-14_CR19.1","doi-asserted-by":"crossref","unstructured":"S. Ramanujan, \"Highly composite numbers\", Proc. London Math. Soc., Series 2, 14, 1915, 347-400","DOI":"10.1112\/plms\/s2_14.1.347"},{"key":"#cr-split#-14_CR19.2","unstructured":"and \"Collected papers\", Cambridge at the University Press, 1927, 78-128."},{"key":"14_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1023\/A:1009764017495","volume":"1","author":"S Ramanujan","year":"1997","unstructured":"S. Ramanujan, \u201cHighly composite numbers, annotated and with a foreword by J.-L. Nicolas and G.\u00a0Robin\u201d, Ramanujan J., 1, 1997, 119\u2013153.","journal-title":"Ramanujan J."},{"key":"14_CR21","first-page":"87","volume":"47","author":"A Selberg","year":"1943","unstructured":"A. Selberg, \u201cOn the normal density of primes in small intervals and the difference between consecutive primes\u201d, Arch. Math. Naturvid, 47, 1943, 87\u2013105.","journal-title":"Arch. Math. Naturvid"},{"key":"14_CR22","first-page":"316","volume":"3","author":"S Shah","year":"1939","unstructured":"S. Shah, \u201cAn Inequality for the Arithmetical Function g(x)\u201d, J. Indian Math. Soc., 3, 1939, 316\u2013318.","journal-title":"J. Indian Math. Soc."},{"key":"14_CR23","first-page":"327","volume":"82","author":"H Siebert","year":"1976","unstructured":"H. Siebert, \u201cMontgomery\u2019s weighted sieve for dimension two\u201d, Monatsch., Math., 82, 1976, 327\u2013336.","journal-title":"Math."},{"key":"14_CR24","unstructured":"N. J. A. Sloane, \u201cThe On-Line Encyclopedia of Integer Sequences\u201d, http:\/\/oeis.org. Accessed 12 December 2012."},{"key":"14_CR25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.4064\/aa-37-1-321-331","volume":"37","author":"M Szalay","year":"1980","unstructured":"M. Szalay, \u201cOn the maximal order in S\n                \n                  n\n                 and \n$$S_{n}^{{\\ast}}$$\n\u201d, Acta Arithmetica, 37, 1980, 321\u2013331.","journal-title":"Acta Arithmetica"},{"key":"14_CR26","unstructured":"http:\/\/math.univ-lyon1.fr\/~nicolas\/landaug.html."}],"container-title":["The Mathematics of Paul Erd\u0151s I"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4614-7258-2_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T12:56:03Z","timestamp":1674132963000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4614-7258-2_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9781461472575","9781461472582"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-1-4614-7258-2_14","relation":{},"subject":[],"published":{"date-parts":[[2013]]},"assertion":[{"value":"20 May 2013","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}