Limitation to the asymptotic formula in Waring's problem
W. K. A. Loh (1996)
Acta Arithmetica
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W. K. A. Loh (1996)
Acta Arithmetica
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J.-L. Nicolas, A. Sárközy (2000)
Journal de théorie des nombres de Bordeaux
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Let denote the number of partitions of into parts, each of which is at least . By applying the saddle point method to the generating series, an asymptotic estimate is given for , which holds for , and .
J. Mikusiński (1953)
Studia Mathematica
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D. Burgess (1971)
Acta Arithmetica
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Andrzej Schinzel (1969)
Acta Arithmetica
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G. A. Camera (1989)
Compositio Mathematica
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Xia Chen, Jay Rosen (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Nobushige Kurokawa, Masato Wakayama (2005)
Rendiconti del Seminario Matematico della Università di Padova
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Michael Drmota, Johannes Gajdosik (1998)
Journal de théorie des nombres de Bordeaux
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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.