Distribution of $m$-core Partition Functions Modulo $M$

• Main Authors: Shih-Wei Chao, 趙世偉
• Other Authors: Wen-Chin Liaw
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/77814531006962460291

碩士 === 國立中正大學 === 數學研究所 === 92 === In this thesis, we are mainly concerned with the $m$-core partition function of $n$, denoted by $C_m(n)$. Using the methods of modular form, we have proved that for $m \geq 5$ prime, there are infinitely many integers $n$ for which $C_m(n) \equiv r \pmod M$ for every residue class $r \pmod M$, here $M$ is what we defined to be an $m$-core good integer. Furthermore, we also give the quantitative result for such $n$.