28 citations · 35 across the 13 of their papers we have counts for
14 papers
Effective Upper Bound Estimates for via Exponential Sums
Ting Liu, Jinjin Ma, Binjie Chang +1
In this paper, we use methods of exponential sums to derive a formula for estimating effective upper bounds of . Different effective upper bounds can be obtained by c…
Values and recurrence relations for integrals of powers of arctan and logarithm and associated Euler-like sums
Xiaoyu Liu, Xinhua Xiong
In this paper, we give evaluations of integrals involving the arctan and the logarithm functions, and present several new summation identities for odd harmonic numbers and Milgram…
A note on values of hypergeometric functions
Xinhua Xiong, Kunzhen Zhang
In this note, we firstly establish an extended Gauss's summation identity. Using this identity, we compute values of a family of hypergeometric functions, which generalize…
A character of Siegel modular group of level 2 from theta constants
Xinhua Xiong
Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are also obtained. By using our theorems, some key theorems o…
Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
XinHua Xiong, William J. Keith
We generalise Euler's partition theorem involving odd parts and different parts for all moduli and provide new companions to Rogers-Ramanujan- Andrews-Gordon identities related to…
Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
Xinhua Xiong, William J. Keith
In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family par…
Small Values of Coefficients of a Half Lerch Sum
Xinhua Xiong
Andrews, Dyson and Hickerson proved many interesting properties of coefficients for a Ramanujan's -hypergeometric series by relating it to real quadratic field $\Q(\sqrt{6})$ an…
A positivity conjecture related first positive rank and crank moments for overpartitions
Xinhua Xiong
Recently, Andrews, Chan, Kim and Osburn introduced a -series for the study of the first positive rank and crank moments for overpartitions. They conjectured that for all…
Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
Xinhua Xiong
In this note, we will give proofs of two congruences involving broken 3-diamond partitions and broken 5-diamond partitions which were conjectured by Peter Paule and Silviu Radu.
A short proof of an identity for cubic partitions
Xinhua Xiong
In this note, we will give a short proof of an identity for cubic partitions.
Congruences for an arithmetic function from 3-colored Frobenius partitions
Laizhong Song, Xinhua Xiong
Let defined by In this note, we prove that for every non-negative integer , a(15n+6) \e…
Congruences modulo powers of 5 for three-colored Frobenius partitions
Xinhua Xiong
Motivated by a question of Lovejoy \cite{lovejoy}, we show that three-colored Frobenius partition function and related arithmetic fuction $\cc3$ vanish modulo some powers of…
The number of cubic partitions modulo powers of 5
Xinhua Xiong
The notion of cubic partitions is introduced by Hei-Chi Chan and named by Byungchan Kim in connection with Ramanujan's cubic continued fractions. Chan proved that cubic partition f…
Ramanujan-Type congruences for cubic partition functions
Xinhua Xiong
The cubic partitions of a natural number , introduced by Chan and Kim, have generating function In th…