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Eisenstein series of 3/2 weight and one conjecture of Kaplansky |
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| Authors: | WANG Xueli PEI Dingyi |
| Affiliation: | 1. Department of Mathematics, Guangzhou University, Guangzhou 510405, China 2. Department of Mathematics, Guangzhou University, Guangzhou 510405, China;State Key Lab of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100039, China |
| Abstract: | We shall prove thatf 1 =x 2 +y 4 + 7z 2 represents all eligible numbers congruent to 2 mod 3 except 14 × 72k which was conjectured by Kanplansky. Our method is to use modular forms of weight 3/2. Our method can also be applied to other ternary quadratic forms. |
| Keywords: | Eisenstein series 3/2 weight Kaplansky conjecture |
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