The representation of the ternary quadratic forms

• Main Authors: Jui-EnChang, 張睿恩
• Other Authors: Po-Yi Huang
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/h3kc5t

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 104 === We will show that all sums of three squares are not universal, and introduce the Gauss and Legendre theorems. We will also give a method to check if a triple sum of squares is regular or irregular. Then, we will study the ternary quadratic forms of mixed sums of squares and triangular numbers. We will show that there are only nitely ternary forms of mixed sums of squares and triangular numbers in each three types which is universal. Finally, we will introduce some methods to determine the ternary quadratic forms of mixed sums of squares and triangular numbers is asymptotically universal or almost universal.