實二次域上的p進L函數的模符號構造

Abstract

在 [DD06] 中，作者給出了在 Qp2-{(0,0)} 上的一個p進測度來定義Λ進艾森斯坦模符號，並當p是慣性於F時，通過計算Λ進艾森斯坦模符號在附加於理想類群的閉鏈上的值來構造實二次域F上的p進L函數。我們將此結果推廣到p是分裂於F的情況，並藉由計算艾森斯坦級數的周期積分來獲得p進L函數的插值公式。

In [DD06], the authors proposed a family of p-adic measures on Qp2-{(0,0)} to define the Λ-adic Eisenstein modular symbol, and constructed the p-adic L-function for a real quadratic field F by evaluating the Λ-adic Eisenstein modular symbol at cycles attached to ideal classes of F for p inert in F. We generalize this result to include the case that p is split in F, and to provide explicit interpolation formulae of the p-adic L-function for F by evaluating explicitly the period integral of Eisenstein series over real quadratic fields.