$p$-adic L-functions of automorphic forms and exceptional zeros
$p$-adic L-functions of automorphic forms and exceptional zeros
复制标题
自守形式和异常零的 $p$-adic L-函数
作者：
H. Deppe
设F是数域，p是素数.我们构造了$GL_2（A_F）$的自守表示的（多变量）p-adic L-函数（在p和$infty$以上的地方有一定的条件），它在中心临界点插值复L-函数。我们使用这种结构来证明，P-进L-函数的模椭圆曲线E在F的消失阶大于或等于素数以上的P，在E分裂乘法减少，预测的例外零猜想。
这是Spie{ss}（arXiv：1207.2289）在全真实的域上的类似结果的推广.
Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $infty$), which interpolates the complex L-function at the central critical point. We use this construction to prove that the p-adic L-function of a modular elliptic curve E over F has vanishing order greater or equal to the number of primes above p at which E has split multiplicative reduction, as predicted by the exceptional zero conjecture.
This is a generalization of analogous results by Spie{ss} (arXiv:1207.2289) over totally real fields.