Eisenstein Cohomology and the Construction of p-Adic Analytic L-Functions
Eisenstein Cohomology and the Construction of p-Adic Analytic L-Functions
复制标题
爱森斯坦上同调和 p-ADIC 解析 L-函数的构造
作者：
J. Mahnkopf
设π是Gl3(
$$mathbb{A}_mathbb{Q}$$
)，在无穷远处上同调类型的pand处未分枝。我们构造了p元L函数，它插值L(π，S)的临界值，并且满足对数增长条件。我们得到了这些函数作为某些分布μπ在ℤp*上的p-进Mellin变换，这些函数在某些固定数域中有值，并且具有中等的增长性。在p-普通情形下，我们得到了开子集Uμπ(U)|p≤|μHaar(U)|p的界|≤ℤp*，其中μHaar表示ℤp*上的不变分布。
AbstractLet π be a cuspidal automorphic representation of GL3(
$$mathbb{A}_mathbb{Q}$$
), unramified at pand of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(π,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions μπon ℤp*having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |μπ(U)|p≤|μHaar(U)|pfor open subsets U≤ ℤp*, where μHaardenotes the invariant distribution on ℤp*.