2-universal Hermitian lattices over imaginary quadratic fields
β Scribed by Myung-Hwan Kim; Poo-Sung Park
- Publisher
- Springer US
- Year
- 2010
- Tongue
- English
- Weight
- 390 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1382-4090
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π SIMILAR VOLUMES
Let L be a positive definite binary integral hermitian lattice over an imaginary quadratic field, and let E(L) denote the number of integers (possibly infinite) which are represented by all localizations of L but not by L itself. It is shown that E(L) tends to infinity as the volume of L tends to in
We consider the family of relative Thue equations where the parameter t, the root of unity Β΅ and the solutions x and y are integers in the same imaginary quadratic number field. We prove that there are only trivial solutions (with |x|, |y| β€ 1), if |t| is large enough or if the discriminant of the