Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-30T18:23:56.817Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 ,

Information

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

Footnotes

The preparation of this paper was supported (in part) by the Office of Naval Research.

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