January 1, 1957Open Access

Congruences for the Coefficients of Modular forms and Some New Congruences for the Partition Function

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Abstract

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, 14, 26. Let p be a prime greater than 3 such that r ( p + l) / 24 is an integer, and set Δ = r ( p 2 − l)/24.

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Morris Newman

California Institute of Technology

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Canadian Journal of Mathematics

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National Institute of Standards and Technology

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Morris Newman (Tue,) studied this question.

synapsesocial.com/papers/69dd6792c5e71f7918100ffe — DOI: https://doi.org/10.4153/cjm-1957-062-1

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

On a conjecture of Ramanujan· 1936 · 1 citations
Identities analogous to Ramanujan’s identities involving the parition function· 1939 · 27 citations
Some Theorems About pr(n)· 1957 · 27 citations
A Table of Ramanujan's Function τ(n)· 1949 · 14 citations
The coefficients of certain infinite products· 1953 · 13 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

On a conjecture of Ramanujan· 1936 · 1 citations
Identities analogous to Ramanujan’s identities involving the parition function· 1939 · 27 citations
Some Theorems About pr(n)· 1957 · 27 citations
A Table of Ramanujan's Function τ(n)· 1949 · 14 citations
The coefficients of certain infinite products· 1953 · 13 citations

Congruences for the Coefficients of Modular forms and Some New Congruences for the Partition Function

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Abstract

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Authors

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