Kim–Lim–Lovejoy congruence conjecture for the mock theta function A(q)

From papers

Let NA(n)N_A(n) be defined by

A(q)=n=0NA(n)qn.A(q)=\sum_{n=0}^{\infty}N_A(n)q^n.

Let p≢7(mod8)p\not\equiv7\pmod8 be an odd prime, let δp\delta_p satisfy

8δp1(modp2),8\delta_p\equiv1\pmod{p^2},

and let k,nZk,n\in\mathbb Z with (kp)=1\left(\frac{k}{p}\right)=1. Kim–Lim–Lovejoy's A(q)A(q) congruence conjecture. Then

NA(p2n+(pk+1)δp)0(mod4).N_A\bigl(p^2n+(pk+1)\delta_p\bigr)\equiv0\pmod4.

This is a mod 44 congruence for coefficients of the second-order mock theta function A(q)A(q). The paper states the conjecture in connection with the odd-balanced unimodal sequence generating function, but the supplied text gives no explicit resolution status.

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Sources & referencesView supporting material

Primary source

Rong Chen and Frank Garvan, “A proof of the mod 4 unimodal sequence conjectures and related mock theta functions”, arXiv:2010.14315 (2020).

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