We prove consequences of functional equations of p-adic L-functions for elliptic curves at supersingular primes p. The results include a relationship between the leading and sub-leading terms (for which we use ideas of Wuthrich and Bianchi), a parity result of orders of vanishing, and invariance of Iwasaswa invariants under conjugate twists of the p-adic L-functions.

中文翻译：

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p-adic L-函数对的函数方程的后果

我们证明了超奇异素数 p 处椭圆曲线的 p-adic L 函数的函数方程的结果。结果包括主导项和次主导项之间的关系（我们使用 Wuthrich 和 Bianchi 的思想）、消失阶的奇偶结果以及在 p-adic L 函数的共轭扭曲下 Iwasaswa 不变量的不变性。