Elementary proofs of relations between Eisenstein series
Elementary proofs of relations between Eisenstein series
复制标题
爱森斯坦级数之间关系的基本证明
DOI：
10.1017/s0308210500013925
复制
发表时间：
1977
期刊：
影响因子：
--
通讯作者：
R. Rankin
中科院分区：
文献类型：
--
作者：
R. Rankin
爱森斯坦级数是具有偶数整数权k <$4的整模形式Ek，其傅里叶展开式由（1.1）给出。有许多恒等式，例如E8 =，与这些级数相关。这些通常是证明的论点，利用维数的向量空间的模形式，而不是直接。本文通过研究不定方程x η +yη = n的解链，说明了如何用初等方法证明这类恒等式.
Synopsis Eisenstein series are entire modular forms Ek of even integral weight k≧ 4 with Fourier expansions given by (1.1). There are numerous identities, such as E8 = , relating these series. These are usually proved by arguments making use of the dimensions of vector spaces of modular forms, and not directly. The paper shows how such identities can be proved by elementary methods by studying chains of solutions of Diophantine equations of the form xξ+yη = n.