Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra
From MaRDI portal
Publication:2070374
DOI10.1007/s11139-021-00506-8zbMath1486.11125arXiv1805.01103OpenAlexW3209443998WikidataQ113900566 ScholiaQ113900566MaRDI QIDQ2070374
Publication date: 24 January 2022
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.01103
Symbolic computation and algebraic computation (68W30) Partitions; congruences and congruential restrictions (11P83) Differential algebra (12H05)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An algorithmic approach to Ramanujan's congruences
- Congruence properties of \(\sigma_ r(N)\)
- Differential Gröbner bases in one variable and in the partial case
- Relations between the ranks and cranks of partitions
- Extension of a proof of the Ramanujan congruences for multipartitions
- Bernoulli identities and combinatoric convolution sums with odd divisor functions
- Infinite families of congruences modulo 7 for Ramanujan's general partition function
- Congruences modulo powers of 5 for \(k\)-colored partitions
- Distribution of the partition function modulo \(m\)
- A short and simple proof of Ramanujan's \(\mod 11\) partition congruence
- Congruences of multipartition functions modulo powers of primes
- New order bounds in differential elimination algorithms
- One-element differential standard bases with respect to inverse lexicographical orderings
- Generalization of Ramanujan's congruences \(p(5m+4)\equiv 0\pmod 5\) and \(p(7m+5)\equiv 0\pmod 7\)
- Ramanujan’s Elementary Method in Partition Congruences
- Congruences modulo powers of 11 for some partition functions
- Congruences for the Coefficients of Modular forms and Some New Congruences for the Partition Function
- Ramanujan Congruences For p-k(n) Modulo Powers Of 17
- A Survey of Multipartitions Congruences and Identities
- Euler's Pentagonal Number Theorem
- Congruence properties for the partition function
- CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS II
- RAMANUJAN'S CONGRUENCES FOR THE PARTITION FUNCTION MODULO 5, 7, AND 11
- CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS
- An elementary proof of p(11m+6)≡0 (mod 11)
- Congruences for p r (n) and Ramanujan's τ Function
This page was built for publication: Computer-assisted proofs of congruences for multipartitions and divisor function convolutions, based on methods of differential algebra