Parity results for certain partition functions and identities similar to theta function identities
Authors:
Richard Blecksmith, John Brillhart and Irving Gerst
Journal:
Math. Comp. 48 (1987), 2938
MSC:
Primary 11P76
MathSciNet review:
866096
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Abstract: In this paper we give a collection of parity results for partition functions of the form and for various sets of positive integers S, which are specified with respect to a modulus, and quadratic polynomials and . Several identities similar to theta function identities, such as and its associated congruence are also proved.
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 R. Blecksmith, John Brillhart & Irving Gerst, "A computerassisted investigation of Ramanujan pairs," Math. Comp., v. 46, 1986, pp. 731749. MR 829643 (87j:11111)
 [2]
 R. Blecksmith, John Brillhart & Irving Gerst, "Partition function parity theorems and theta function identity analogues," Abstracts Amer. Math. Soc., v. 7, 1986, p. 225.
 [3]
 L. Carlitz & M. V. Subbarao, "A simple proof of the quintuple product identity," Proc. Amer. Math. Soc., v. 32, 1972, pp. 4244. MR 0289316 (44:6507)
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 B. Gordon, "Some identities in combinatorial analysis," Quart. J. Math. Oxford Ser. (2), v. 12, 1961, pp. 285290, MR 25 #2340. MR 0136551 (25:21)
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 P. A. MacMahon, Collected Papers, vol. 1, MIT Press, Cambridge, Mass., 1978. MR 514405 (80k:01065)
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 T. R. Parkin & D. Shanks, "On the distribution of parity in the partition function," Math. Comp., v. 21, 1967, pp. 466480. MR 0227126 (37:2711)
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 M. V. Subbarao, "Some remarks on the partition function," Amer. Math. Monthly, v. 73, 1966, pp. 851854. MR 0201409 (34:1293)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819870866096X
PII:
S 00255718(1987)0866096X
Keywords:
Partition function parity,
theta function analogues
Article copyright:
© Copyright 1987 American Mathematical Society
