On the reciprocation of infinite modularpart products and the parity of certain partition functions
Authors:
Richard Blecksmith, John Brillhart and Irving Gerst
Journal:
Math. Comp. 54 (1990), 345376
MSC:
Primary 05A17; Secondary 05A30
MathSciNet review:
995206
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Abstract: An infinite, modularpart (MP) product is defined to be a product of the form , where . Some products of this kind have a reciprocal that is also an MP product, while others do not. A complete method is first developed which determines if a given MP product has an MP reciprocal modulo 2 and finds it if it does. Next, a graphtheoretic interpretation of this method is made from which a streamlined algorithm is derived for deciding whether the given MP product is such a reciprocal. This algorithm is then applied to the singlevariable Jacobi triple product and the quintuple product to determine the cases when these products have an MP reciprocal . When this occursand this occurs in infinitely many casesthe parity of the associated partition function can readily be found. A discussion is also made of the probability that a given MP product with modulus m has an MP reciprocal .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199009952069
PII:
S 00255718(1990)09952069
Keywords:
reciprocation,
infinite modularpart products,
Jacobi triple product,
quintuple product
Article copyright:
© Copyright 1990
American Mathematical Society
