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Some Theorems About pr(n)

Published online by Cambridge University Press:  20 November 2018

Morris Newman
Morris Newman*
Affiliation:
National Bureau of Standards, Washington, D.C.
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If n is a non-negative integer, define pr(n) as the coefficient of xn in

;

otherwise define pr(n) as 0. In a recent paper (1) the author has proved that if r has any of the values 2, 4, 6, 8, 10, 14, 26 and p is a prime > 3 such that r(p + 1) ≡ 0 (mod 24), then

1, ,

where n is an arbitrary integer.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 68 - 70
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Newman, M., An identity for the coefficients of certain modular forms. J. Lond. Math. Soc, 30 (1955), 488–493.Google Scholar
2. van der Pol, B., The representation of numbers as sums of eight, sixteen, and twenty-four squares, Proc. Kon. Nederl. Akad. Wetensch. Ser. A 57 — Indagationes Math. 16 (1954), 349–361.Google Scholar