Ernest X. W. Xia

A PROOF OF KEITH'S CONJECTURE FOR 9-REGULAR PARTITIONS MODULO 3

Let bt(n) denote the number of t-regular partitions of n. Recently, Keith discovered some congruences modulo 3 for 9-regular partitions. He also conjectured that In this note, we confirm this conjecture by employing some identities given by Ramanujan and Hirschhorn.

Evaluation of the convolution sum ∑i+25j=n σ(i)σ(j)

In this paper, the convolution sum ∑i+25j=n σ(i)σ(j) is evaluated for all n ∈ ℕ based on some identities due to Berndt, Lemire and Williams.

2-Log-Concavity of the Boros–Moll Polynomials

The Boros-Moll polynomials

EXPLICIT FORMULAS FOR THE FOURIER COEFFICIENTS OF A CLASS OF ETA QUOTIENTS

P_m(a)

EVALUATION OF THE CONVOLUTION SUMS ∑i+3j=nσ(i)σ3(j) AND ∑3i+j=nσ(i)σ3(j)

arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that

A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

P_m(a)

ON THE REPRESENTATIONS OF INTEGERS BY CERTAIN QUADRATIC FORMS

is 2-log-concave for any

CONGRUENCES MODULO POWERS OF 2 FOR FU’S 5 DOTS BRACELET PARTITIONS

m\geq 2

The signs of three-term recurrence sequences

. Let

THE 8-DISSECTION OF THE RAMANUJAN–GÖLLNITZ–GORDON CONTINUED FRACTION BY AN ITERATIVE METHOD

d_i(m)