Abstract
Let 
be a real quadratic field with m a square-free positive rational integer, and 
be the ring of integers in F. An -lattice L on a totally positive definite quadratic space V over F is called r-universal if L represents all totally positive definite -lattices l with rank r over . We prove that there exists no 2-universal -lattice over F with rank less than 6, and there exists a 2-universal -lattice over F with rank 6 if and only if m=2, 5. Moreover there exists only one 2-universal -lattice with rank 6, up to isometry, over 
.
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Sasaki, H. 2-universal 
-lattices over real quadratic fields.
manuscripta math. 119, 97–106 (2006). https://doi.org/10.1007/s00229-005-0607-9
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DOI: https://doi.org/10.1007/s00229-005-0607-9