Analogues of Ramanujan's partition identities and congruences arising from his theta functions and modular equations
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Publication:693018
DOI10.1007/s11139-011-9296-zzbMath1254.05023OpenAlexW2164264180MaRDI QIDQ693018
Nayandeep Deka Baruah, Kanan Kumari Ojah
Publication date: 7 December 2012
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-011-9296-z
Partitions; congruences and congruential restrictions (11P83) Theta series; Weil representation; theta correspondences (11F27) Partition identities; identities of Rogers-Ramanujan type (11P84)
Related Items (41)
Congruences for Andrews' singular overpartitions ⋮ Arithmetic properties of (2, 3)-regular overcubic bipartitions ⋮ Parity results for 7-regular and 23-regular partitions ⋮ Arithmetic properties of 5-tuple partitions with 3-cores ⋮ Partition identities arising from Ramanujan's formulas for multipliers ⋮ Congruences modulo 16, 32, and 64 for Andrews's singular overpartitions ⋮ Analogues of Ramanujan's partition identities ⋮ New congruences for \(t\)-core partitions and Andrews' singular overpartitions ⋮ The number of tagged parts over the partitions with designated summands ⋮ Arithmetic properties of singular overpartition pairs without multiples of k ⋮ On 9-regular bipartitions with distinct even parts ⋮ New parity results for broken 11-diamond partitions ⋮ New congruences modulo powers of 2 and 3 for 9-regular partitions ⋮ Arithmetic density and new congruences for \(3\)-core partitions ⋮ Arithmetic properties of bipartitions with 3-cores ⋮ Some congruences for overpartitions with restriction ⋮ CONGRUENCESFORBIPARTITIONSWITHODDDESIGNATED SUMMANDS ⋮ Double coset operators and eta-quotients ⋮ Arithmetic properties of 5-regular bipartitions ⋮ Parity results for 9-regular partitions ⋮ Congruences for Andrews singular overpartition pairs ⋮ Some congruence properties of a restricted bipartition function \(c_N(n)\) ⋮ Arithmetic properties of bipartitions with designated summands ⋮ Color partition identities arising from Ramanujan's theta-functions ⋮ Congruences modulo 9 and 27 for overpartitions ⋮ Congruences for \(\ell \)-regular overpartitions and Andrews' singular overpartitions ⋮ RAMANUJAN-TYPE CONGRUENCES FOR SEVERAL PARTITION FUNCTIONS ⋮ Ramanujan-type congruences modulo 8 for 7- and 23-core partition functions ⋮ Congruences for a certain partition function ⋮ Some new congruences for Andrews' singular overpartition pairs ⋮ Unnamed Item ⋮ Some new congruences for Andrews' singular overpartitions ⋮ Unnamed Item ⋮ Congruences for overpartitions with restricted odd differences ⋮ Arithmetic properties of partitions with designated summands ⋮ Unnamed Item ⋮ Arithmetic properties of 9-regular partitions with distinct odd parts ⋮ Parity results for broken 5-diamond, 7-diamond and 11-diamond partitions ⋮ Arithmetic properties for Fu's 9 dots bracelet partitions ⋮ Multiranks and classical theta functions ⋮ Congruences for \(\ell\)-regular overpartitions into odd parts
Cites Work
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- Partition identities arising from theta function identities
- Congruences modulo powers of 2 for a certain partition function
- New analogues of Ramanujan's partition identities
- Several identities for certain products of theta functions
- A few theta-function identities and some of Ramanujan's modular equations
- Partition-theoretic interpretations of certain modular equations of Schröter, Russell, and Rama\-nujan
- Some new proofs of modular relations for the Göllnitz-Gordon functions
- Partition identities and Ramanujan's modular equations
- RAMANUJAN'S CUBIC CONTINUED FRACTION AND AN ANALOG OF HIS "MOST BEAUTIFUL IDENTITY"
- RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION
- Proof of a conjecture of Ramanujan
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