6 papers · 1 filter
Lower bound estimates for the rank of universal quadratic forms in some families of real cubic fields with density one
Liwen Gao, Xuejun Guo
In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of densit…
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.