arXiv subjects

Su-Ping Cui

Publications and source records attributed to Su-Ping Cui.

3 recordsLinked to original sources

arXiv2026

Two Proofs of a Conjecture of Amdeberhan, Andrews and Ballantine for double Lambert series and a new Representation for $E_2(q)$

In this note, we prove a recent conjecture of Amdeberhan, Andrews and Ballantine concerning a double Lambert series (\textit{J. Combin. Theory Series A} \textbf{221} (2026), Paper No. 106154). More precisely, they conjectured that \[ [q^{N2^a}] \sum_{m,k\geq 1} \frac{q^{mk2^a}}{(1+q^{k2^{a-1}})(1-q^{2m-1})} =\sigma_1(N), \] where $\sigma_1(N)$ is the sum of all the positive divisors of $N$. We provide two proofs of this conjecture. One of the approach leads us to derive a new representation of quasi-modular forms $E_2(q)$.

math.NT↗

arXiv2026

Identities and transformations for Lambert series and double Lambert series

We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andrews and Ballantine (J Combin Theory Series A 221:106154, 2026). The proofs are based on classical transformations in the theory of infinite series together with a systematic rearrangement of double Lambert series.

math.NT↗

arXiv2018

Four identities related to third order mock theta functions

Ramanujan presented four identities for third order mock theta functions in his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first proved these four identities. Recently, Andrews et al. provided different proofs by using $q$-series. In this paper, in view of some identities of a universal mock theta function \begin{align*} g(x;q)=x^{-1}\left(-1+\sum_{n=0}^{\infty}\frac{q^{n^{2}}}{(x;q)_{n+1}(qx^{-1};q)_{n}}\right), \end{align*} we establish new proofs of these four identities. In particular, by means of an identity of $g(x;q)$ given by Ramanujan and some theta function identities due to Mortenson, we find a new simple proof of the fourth identity.

math.CO↗