A root of unity occurring in partition theory
Author:
Peter Hagis
Journal:
Proc. Amer. Math. Soc. 26 (1970), 579-582
MSC:
Primary 10.48
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265308-2
MathSciNet review:
0265308
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper a new representation is found for the root of unity occurring in the well-known transformation equation of the generating function for $p(n)$, the number of partitions of the positive integer $n$.
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G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115.
H. Rademacher, Zur Theorie der Modulfunktionen, J. Reine Angew. Math. 167 (1931), 312-336.
H. Rademacher, On the partition function $p(n)$, Proc. London Math. Soc. (2) 43 (1937), 241-254.
- Hans Rademacher and Albert Whiteman, Theorems on Dedekind sums, Amer. J. Math. 63 (1941), 377–407. MR 3650, DOI https://doi.org/10.2307/2371532
- Hans Rademacher, On the Selberg formula for $A_k(n)$, J. Indian Math. Soc. (N.S.) 21 (1957), 41–55 (1958). MR 92818
- Albert Leon Whiteman, A sum connected with the series for the partition function, Pacific J. Math. 6 (1956), 159–176. MR 80122
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Additional Information
Keywords:
Partitions,
generating function,
transformation equation,
roots of unity
Article copyright:
© Copyright 1970
American Mathematical Society