DERIVATIVE OF THE STANDARD p-ADIC L-FUNCTION ASSOCIATED WITH A SIEGEL FORM.

In this paper we first construct a two-variable p-adic L-function for the standard representation associated with a Hida family of parallel weight genus g Siegel forms, using a method developed by Böcherer-Schmidt in one variable. When a form f has weight g + 1 a non-crystalline trivial zero could appear. In this case, using the two-variable p-adic L-function we have constructed, we can apply the method of Greenberg-Stevens to calculate the first derivative of the p-adic L-function for f and show that it has the form predicted by a conjecture of Greenberg on trivial zeros. [ABSTRACT FROM AUTHOR]