论文标题
Theta系列的三元二次晶格cosets
Theta series of ternary quadratic lattice cosets
论文作者
论文摘要
在本文中，我们考虑了theta系列的分解，用于三元格的晶格曲线。我们表明，自然分解为爱森斯坦系列，一个theta函数和一种cuspidal形式，它与一般theta的函数正交，对应于该属的theta系列，theta系列的不足，用于属属的旋律属，以及theta server的缺陷，以及theta serverty serveral of Spinor spinor spinor spinor spinor n n n spinor n spinor n eg spine cen n eg spine cen n eg spine cen n eg spine cen n of a n a spine n of a spinor a spine n s of a n sap n of of a spinor。因此，这三个部分分别是属，纺纱属和阶级的不变，扩展了已知的晶格结果，并验证了第一作者和Haensch的猜想。此外，我们将$ p $ -Neighbors的定义扩展到包括晶格cosets并构建算法，以通过$ p $ neighborhoods来计算属或纺纱属中的类别的重新表现。
In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary theta functions correspond to the theta series for the genus, the deficiency of the theta series for the spinor genus from that of the genus, and the deficiency of the theta series for the class from that of the spinor genus, respectively. These three pieces are hence invariants of the genus, spinor genus, and class, respectively, extending known results for lattices and verifying a conjecture of the first author and Haensch. We furthermore extend the definition of $p$-neighbors to include lattice cosets and construct an algorithm to compute respresentatives for the classes in the genus or spinor genus via the $p$-neighborhoods.
