Further Identities and Congruences for the Coefficients of Modular Forms

@article{Newman1958FurtherIA,
  title={Further Identities and Congruences for the Coefficients of Modular Forms},
  author={Morris Newman},
  journal={Canadian Journal of Mathematics},
  year={1958},
  volume={10},
  pages={577 - 586}
}
  • M. Newman
  • Published 1958
  • Mathematics
  • Canadian Journal of Mathematics
If n is a non-negative integer, define p r(n) by otherwise define p r(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.) p r(n) is thus generated by the powers of , 
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  • A. Atkin
  • Mathematics
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  • 1967
We write and so that p(n) is the number of unrestricted partitions of n. Ramanujan [1] conjectured in 1919 that if q = 5, 7, or 11, and 24m ≡ 1 (mod qn), then p(m) ≡ 0 (mod qn). He proved his
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References

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Arithmetic of Quaternions
On the Existence of Identities for the Coefficients of Certain Modular Forms
Identities analogous to Ramanujaris identities involving the partition function
  • Duke Math. J.,
  • 1939
Congruences for the Coefficients of Modular forms and Some New Congruences for the Partition Function
  • M. Newman
  • Mathematics
    Canadian Journal of Mathematics
  • 1957
If n is a non-negative integer, define p r(n) as the coefficient of x n in ; otherwise define p r(n) as 0. In a recent paper (2) the author established the following congruence: Let r = 4, 6, 8, 10,