8 papers
Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotients
Jing Jin, Olivia X. M. Yao, Shiwen Zhou
Bringmann, Han, Heim, and Kane recently investigated periodic sign patterns in the Fourier coefficients of weakly holomorphic modular forms arising from eta-quotients and posed num…
A proof of the Baruah--Gogoi conjecture on sums of odd and even overlined parts
Eric H. Liu, X. L. Liu, Olivia X. M. Yao
Andrews and Dastidar introduced the statistic $\SOME(n)$, defined as the difference between the sum of all odd parts and the sum of all even parts occurring in the partitions of $n…
Proof of a conjecture of Banerjee,Bringmann and Bachraoui on infinite families of congruences
Junjie Sun, Olivia X. M. Yao
Recently, Andrews and Bachraoui investigated congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan type congruences and a vanishing ident…
Some identities on the second order mock theta functions
Xingyuan Cai, Eric H. Liu, Olivia X. M. Yao
Recently, Nath and Das investigated congruence properties for the second order mock theta function . In their paper, they asked for analytic proofs of three identities on the…
Parity results for the reciprocals of false theta functions
Jing Jin, Huan Xu, Olivia X. M. Yao
Recently, Keith investigated arithmetic properties for the reciprocals of some false theta functions and posed several conjectures. In this paper, we prove some parity results for…
Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function
Jing Jin, Sijia Wang, Olivia X. M. Yao
Recently, Keith investigated reciprocals of false theta functions and proved some interesting results such as congruences, asymptotic bounds, and combinatorial identities. At the e…
Proofs of two conjectures on congruences of overcubic partition triples
Jiayu Chen, Jing Jin, Olivia X. M. Yao
Let denote the number of overcubic partition triples of . Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for . Rec…
Congruences modulo arbitrary powers of and for Andrews and Paule's partition diamonds with copies of
Julia Q. D. Du, Olivia X. M. Yao
Recently, Andrews and Paule introduced a partition function which denotes the number of partition diamonds with copies of where summing the parts at the links…