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Congruence properties of partitions

โœ Scribed by S. Ramanujan

Book ID
105170445
Publisher
Springer-Verlag
Year
1921
Tongue
French
Weight
257 KB
Volume
9
Category
Article
ISSN
0025-5874

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๐Ÿ“œ SIMILAR VOLUMES

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The partition function p(n) has several celebrated congruence properties which reflect the action of the Hecke operators on certain holomorphic modular forms. In this article similar congruences are proved for c 3 (n), the number of generalized Frobenius partitions of n with 3 colors. We prove c 3 (

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Simple, uniform proofs are given of Ramanujan's partition congruences p(5n+4)=Omod5, p(7n+5)-Omod7, p(lln+6)=Omodll Also, generating functions are obtained for the partitions involved in Ramanujan's more general congruences.