An algorithmic approach to Ramanujan's congruences
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Publication:1047807
DOI10.1007/s11139-009-9174-0zbMath1204.11165OpenAlexW2066276027MaRDI QIDQ1047807
Publication date: 6 January 2010
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-009-9174-0
Partitions; congruences and congruential restrictions (11P83) Holomorphic modular forms of integral weight (11F11) Analytic theory of partitions (11P82)
Related Items (30)
Ramanujan-style proof of \(p_{-3}(11n+7) \equiv 0 \pmod{11}\) ⋮ A further look at cubic partitions ⋮ Arithmetic properties of cubic and overcubic partition pairs ⋮ PROOF OF SOME CONJECTURAL CONGRUENCES OF DA SILVA AND SELLERS ⋮ Congruences for k-elongated plane partition diamonds ⋮ Certain Diophantine equations and new parity results for 21-regular partitions ⋮ Arithmetic density and new congruences for \(3\)-core partitions ⋮ 4-regular partitions and the pod function ⋮ Arithmetic density and congruences of \(t\)-core partitions ⋮ Congruences for the coefficients of the mock theta function \(\beta (q)\) ⋮ Congruences modulo \(4\) for the number of \(3\)-regular partitions ⋮ Congruences and recursions for the cubic partition ⋮ Congruences for the coefficients of a pair of third and sixth order mock theta functions ⋮ Congruences modulo powers of 2 for restricted partition triples due to Lin and Wang ⋮ An algorithmic approach to Ramanujan-Kolberg identities ⋮ On the computation of identities relating partition numbers in arithmetic progressions with eta quotients: an implementation of Radu's algorithm ⋮ On the parity of broken \(k\)-diamond partitions ⋮ Unnamed Item ⋮ Congruences for 1-shell totally symmetric plane partitions ⋮ New congruences for 2-color partitions ⋮ An extensive analysis of the parity of broken 3-diamond partitions ⋮ Finding modular functions for Ramanujan-type identities ⋮ Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra ⋮ CONGRUENCE PROPERTIES MODULO 5 AND 7 FOR THE pod FUNCTION ⋮ Proof of a conjecture by Ahlgren and Ono on the non-existence of certain partition congruences ⋮ Divisibility of certain \(\ell\)-regular partitions by 2 ⋮ An algorithm to prove holonomic differential equations for modular forms ⋮ Proofs of five conjectures on matching coefficients of Baruah, Das and Schlosser by an algorithmic approach ⋮ ARITHMETIC PROPERTIES OF -REGULAR BIPARTITIONS ⋮ A proof of Subbarao's conjecture
Cites Work
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- Some congruences for Andrews-Paule's broken 2-diamond partitions
- Spiral waves for the 2D Riemann problem for a compressible fluid
- Computational proofs of congruences for \(2\)-colored Frobenius partitions
- Congruences for Frobenius partitions
- Some identities involving the partition function
- MacMahon's partition analysis XI: Broken diamonds and modular forms
- On recent congruence results of Andrews and Paule for broken k-diamonds
- The Components of Modular Forms
- Construction and Application of a Class of Modular Functions (II)†
- The Ramanujan Identities Under Modular Substitutions
- Ramanujan-type congruences for three colored Frobenius partitions
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