Results 21 to 30 of about 349 (51)
Partitions which are p- and q-core [PDF]
, 2001 Let p and q be distinct primes, n an integer with n > p2q2. Then there is no partition of n which is at the same time p- and q-core.
Schlage-Puchta, Jan-Christoph
core
Proofs of Some Conjectures of Chan on Appell-Lerch Sums
, 2018 On page 3 of his lost notebook, Ramanujan defines the Appell-Lerch sum $$\phi(q):=\sum_{n=0}^\infty \dfrac{(-q;q)_{2n}q^{n+1}}{(q;q^2)_{n+1}^2},$$ which is connected to some of his sixth order mock theta functions. Let $\sum_{n=1}^\infty a(n)q^n:=\phi(q)$
Baruah, Nayandeep Deka +1 more
core +1 more source
Congruences involving generalized Frobenius partitions
, 1992 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 413-415, 1993.
James Sellers
wiley +1 more source
On the number of solutions of a restricted linear congruence
, 2017 Consider the linear congruence equation $${a_1^{s}x_1+\ldots+a_k^{s} x_k \equiv b\,(\text{mod } n^s)}\text { where } a_i,b\in\mathbb{Z},s\in\mathbb{N}$$ Denote by $(a,b)_s$ the largest $l^s\in\mathbb{N}$ which divides $a$ and $b$ simultaneously.
Namboothiri, K Vishnu
core +1 more source
Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions [PDF]
, 2013 Let $\bar{p}(n)$ denote the number of overpartitions of $n$. It was conjectured by Hirschhorn and Sellers that $\bar{p}(40n+35)\equiv 0\ ({\rm mod\} 40)$ for $n\geq 0$. Employing 2-dissection formulas of quotients of theta functions due to Ramanujan, and
Chen, William Y. C., Xia, Ernest X. W.
core
Arithmetic Properties of Overpartition Pairs [PDF]
, 2010 Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of $\bar{pp}(n)$, the number of overpartition pairs of n.
Chen, William Y. C., Lin, Bernard L. S.
core
A periodic approach to plane partition congruences
, 2015 Ramanujan's celebrated congruences of the partition function $p(n)$ have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational polynomial functions yields a general theorem used to establish congruences
Mizuhara, Matthew S. +2 more
core
Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions. [PDF]
Ann Comb, 2023 Banerjee K, Dastidar MG.
europepmc +1 more source
On sums of coefficients of polynomials related to the Borwein conjectures. [PDF]
Ramanujan J, 2022 Goswami A, Pantangi VRT.
europepmc +1 more source
A single-variable proof of the omega SPT congruence family over powers of 5. [PDF]
Ramanujan J, 2023 Smoot NA.
europepmc +1 more source