2 papers
math.NT2025
Proof of a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of M_{C1}(m,n) and M_{C5}(m,n)
Bing He, Shuming Liu
In their 2016 paper on exotic Bailey--Slater SPT-functions, Garvan and Jennings-Shaffer introduced many new spt-crank-type functions and proposed a conjecture that the spt-crank-ty…
math.NT2025
Weighted partial sums of a random multiplicative function and their positivity
Shuming Liu, Bing He
In this paper, we study the probability that some weighted partial sums of a random multiplicative function are positive. Applying the characteristic decomposition, we obtain t…