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Further Identities and Congruences for the Coefficients of Modular Forms

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) by otherwise define pr(n) as 0. (Here and in what follows all sums will be extended from 0 to ∞ and all products from 1 to ∞ unless otherwise stated.) pr(n) is thus generated by the powers of ,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 577 - 586
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Newman, N., On the existence of identities for the coefficients of certain modular forms, J. Lond. Math. Soc, 31 (1956), 350-359.Google Scholar
2. Newman, N., An identity for the coefficients of certain modular forms, J. Lond. Math. Soc, 30 (1955), 488-493.Google Scholar
3. Newman, N., Remarks on some modular identities, Trans. Amer. Math. Soc, 73 (1952), 313–320.Google Scholar
4. Newman, N., A table of the coefficients of the powers of η(T), Proc Kon. Nederl. Akad. Wetensch., Ser. A 59 = Indag. Math., 18 (1956), 204-216.Google Scholar
5. Newman, N., Congruences for the coefficients of modular forms and some new congruences for the partition function, Can. J. Math., 9 (1957), 549-552.Google Scholar
6. Newman, N., Some theorems about pr(n), Can. J. Math., 9 (1957), 68-70.Google Scholar
7. Pall, G., On the arithmetic of quaternions, Trans. Amer. Math. Soc, 47 (1940), 487-500.Google Scholar
8. Zuckerman, H., Identities analogous to Ramanujaris identities involving the partition function, Duke Math. J., 5 (1939), 88-110.Google Scholar