CM椭圆曲线的超几何函数和周期的特殊值

2017 MATRIX Annals Pub Date : 2015-03-27 DOI:10.1090/TRAN/7134

Yifan Yang

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引用次数: 3

摘要

设\(X=X_0^6(1)/W_6\)为志村曲线\(X_0^6(1)\)的商，通过所有的阿特金-雷纳对合。通过实现X上的两种模形式，一种是超几何函数的模形式，另一种是Borcherds形式的模形式，利用cm点处Borcherds形式值的Schofer公式，用复乘法得到了\(\overline Q\)上椭圆曲线周期的某些超几何函数的特殊值。

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Special Values of Hypergeometric Functions and Periods of CM Elliptic Curves

Let \(X=X_0^6(1)/W_6\) be the quotient of the Shimura curve \(X_0^6(1)\) by all the Atkin-Lehner involutions. By realizing modular forms on X in two ways, one in terms of hypergeometric functions and the other in terms of Borcherds forms, and using Schofer’s formula for values of Borcherds forms at CM-points, we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over \(\overline Q\) with complex multiplication.

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2017 MATRIX Annals

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