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The Kloosterman problem for binary Hermitian lattices |
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| Authors: | Byeong Moon Kim Ji Young Kim Poo-Sung Park |
| Institution: | 1. Department of Mathematics, Gangneung-Wonju National University, 123 Chibyondong, Gangneung, Gangwon-Do, 210-702, Korea 2. Department of Mathematical Sciences, Seoul National University, 1 Gwanakro, Gwanak-gu, Seoul, 151-747, Korea 3. Department of Mathematics Education, Kyungnam University, 449 Wolyong-Dong, Changwon, Kyungnam, 631-701, Korea |
| Abstract: | A Hermitian lattice over an imaginary quadratic field $\mathbb {Q}(\sqrt{-m})$ is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal $p$ -anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices. |
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