Indecomposable quadratic lattices over global function fields
نویسندگان
چکیده
منابع مشابه
Quadratic Forms over Global Fields
1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12...
متن کاملDIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...
متن کاملBinary Normal Regular Hermitian Lattices over Imaginary Quadratic Fields
We call a positive definite Hermitian lattice regular if it represents all integers, which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields Q( √ −m) and provide a complete list of the (normal) binary regular Hermitian lattices.
متن کامل2-universal Hermitian Lattices over Imaginary Quadratic Fields
We call a positive definite integral quadratic form universal if it represents all positive integers. Then Lagrange’s Four Square Theorem means that the sum of four squares is universal. In 1930, Mordell [M] generalized this notion to a 2-universal quadratic form: a positive definite integral quadratic form that represents all binary positive definite integral quadratic forms, and showed that t...
متن کاملSome remarks for codes and lattices over imaginary quadratic fields
Let ` > 0 be a square-free integer, ` ≡ 3 mod 4, K = Q( √ −`), and OK the ring of integers of K. Codes C over rings R := OK/pOK determine lattices Λ`(C) over K. The theta series θΛ`(C) of such lattice can be written in terms of the complete weight enumerator of C. For any `′ > ` the first `+1 4 terms of their corresponding theta functions are the same with those of Λ`(C). In [6] it was conjectu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.09.012