6 papers · 1 filter
Distribution of the k-regular partition function modulo composite integers M
Yiwen Lu, Xuejun Guo
Let denote the regular partitons of a natural number . In this paper, we study the behavior of modulo composite integers which are coprime to . Spec…
An improvement on the parity of Schur's partition function
Yiwen Lu, Tao Wei, Xuejun Guo
We improve S.-C. Chen's result on the parity of Schur's partition function. Let be the number of Schur's partitions of , i.e., the number of partitions of into distin…
The rank of 2-Selmer group associate to -congruent numbers
Tao Wei, Xuejun Guo
We study the parity of rank of - groups associated to and -congruent numbers. Our second result gives some positive densities about and no…
Mahler measures and -values of elliptic curves over real quadratic fields
Zhengyu Tao, Xuejun Guo, Tao Wei
A famous formula of Rodriguez Villegas shows that the Mahler measures of can be written as a Kronecker-Eisenstein series. We prove that the degree o…
Some new Ramanujan-Sato series for
Tao Wei, Zhengyu Tao, Xuejun Guo
We derive 10 new Ramanujan-Sato series of by using the method of Huber, Schultz and Ye. The levels of these series are 14, 15, 16, 20, 21, 22, 26, 35, 39.
The eigenvectors-eigenvalues identity and Sun's conjectures on determinants and permanents
Xuejun Guo, Xin Li, Zhengyu Tao +1
In this paper, we prove a conjecture raised by Zhi-Wei Sun in 2018 by the eigenvectors-eigenvalues identity found by Denton, Parke, Tao and X. Zhang in 2019.