Modular forms of degree n and representation by quadratic forms IV
Modular forms of degree n and representation by quadratic forms IV
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n 次模形式和二次形式 IV 表示
DOI：
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发表时间：
1979
影响因子：
0.8
通讯作者：
Y. Kitaoka
中科院分区：
文献类型：
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作者：
Y. Kitaoka
设M是有理整数环上具有正定二次型的二次格，M‘是有限指数的子模，S是包含2[M：M’]的所有素因子的有限素数集，且使得MP对p∉S是么模的。在文[2]中，我们证明了对每一个具有正定二次型的格N和等距图FP：NP∊MP的集合(FP)p→S，都有一个等距f：N→M对每个p|[M：M]满足f≡FP mod M‘p，对于每一个p∉S，F(NP)在MP中是私有的，只要有最小的N≥c和秩M≥3阶为N+3.
Let M be a quadratic lattice with positive definite quadratic form over the ring of rational integers, M’ a submodule of finite index, S a finite set of primes containing all prime divisors of 2[M: M’] and such that Mp is unimodular for p ∉ S. In [2] we showed that there is a constant c such that for every lattice N with positive definite quadratic form and every collection (fp)p∊s of isometries fp: NP → MP there is an isometry f: N → M satisfying f ≡ fp mod M′p for every p |[M: M], f(Np ) is private in Mp for every p ∉ S, provided the minimum of N ≥ c and rank M ≥ 3 rank N + 3.