Partition functions whose logarithms are slowly oscillating
HTML articles powered by AMS MathViewer
- by S. Parameswaran PDF
- Trans. Amer. Math. Soc. 100 (1961), 217-240 Request permission
References
- András Békéssy, Eine Verallgemeinerung der Laplaceschen Methode, Magyar Tud. Akad. Mat. Kutató Int. Közl. 2 (1957), 105–125 (German, with Russian and Hungarian summaries). MR 97667
- Nelson A. Brigham, A general asymptotic formula for partition functions, Proc. Amer. Math. Soc. 1 (1950), 182–191. MR 34409, DOI 10.1090/S0002-9939-1950-0034409-3 N. G. de Bruijn, On Mahler’s partition problem, Nederl. Akad. Wetensch. Indag. Math., vol. 10 (1948) pp. 210-220.
- N. G. de Bruijn, Pairs of slowly oscillating functions occurring in asymptotic problems concerning the Laplace transform, Nieuw Arch. Wisk. (3) 7 (1959), 20–26. MR 107120
- N. G. de Bruijn and P. Erdös, On a recursion formula and on some Tauberian theorems, J. Research Nat. Bur. Standards 50 (1953), 161–164. MR 0054745
- Hubert Delange, Sur un théorème de Karamata, Bull. Sci. Math. (2) 79 (1955), 9–12 (French). MR 69253
- P. Erdös, On an elementary proof of some asymptotic formulas in the theory of partitions, Ann. of Math. (2) 43 (1942), 437–450. MR 6749, DOI 10.2307/1968802
- G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620 G. H. Hardy and S. Ramanujan, Asymptotic formulae for the distribution of integers of various types, Proc. London Math. Soc. vol. 16 (1917) pp. 112-132. J. Karamata, Sur un mode de croissance régulière des fonctions, Mathematica (Cluj) vol. 4 (1930) pp. 38-53. K. Knopp, Asymptotische formeln der additiven Zahlentheorie, Schriften der Köningsberger Gelehrten Gesellschaft Naturwissenschaftliche Klasse vol. 3 (1925) pp. 45-74.
- Eugene E. Kohlbecker, Weak asymptotic properties of partitions, Trans. Amer. Math. Soc. 88 (1958), 346–365. MR 95808, DOI 10.1090/S0002-9947-1958-0095808-9
- J. Korevaar, T. van Aardenne-Ehrenfest, and N. G. de Bruijn, A note on slowly oscillating functions, Nieuw Arch. Wiskunde (2) 23 (1949), 77–86. MR 0027812
- Kurt Mahler, On a special functional equation, J. London Math. Soc. 15 (1940), 115–123. MR 2921, DOI 10.1112/jlms/s1-15.2.115
- W. B. Pennington, On Mahler’s partition problem, Ann. of Math. (2) 57 (1953), 531–546. MR 53959, DOI 10.2307/1969735
Additional Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 100 (1961), 217-240
- MSC: Primary 10.48
- DOI: https://doi.org/10.1090/S0002-9947-1961-0140498-X
- MathSciNet review: 0140498