The universality of -functions associated with new forms
The universality of -functions associated with new forms
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与新形式相关的功能的普遍性
DOI：
10.1070/im2003v067n01abeh000419
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Steuding
中科院分区：
文献类型：
--
作者：
A. Laurinčikas;Kohji Matsumoto;J. Steuding
证明了新抛物型-函数的通用性定理。它涉及解析函数通过这些-函数的移位的一致逼近。该定理与Shimura-Taniyama猜想（现已证明）一起得出非奇异椭圆曲线-函数在有理数域上的通用性。函数的通用性意味着它们在函数上是独立的。
We prove the universality theorem for -functions of new parabolic forms. It concerns the uniform approximation of analytic functions by shifts of these -functions. This theorem together with the Shimura-Taniyama conjecture (now proved) yields the universality of -functions of non-singular elliptic curves over the field of rational numbers. The universality of -functions implies that they are functionally independent.