Derivative of the standard $p$-adic $L$-function associated with a Siegel form

Abstract

In this paper we construct a two variables $p$-adic $L$-function for the standard representation associated with a Hida family of parallel weight genus $g$ Siegel forms, using a method previously developed by Böcherer--Schmidt in one variable. When a form of weight $g+1$ is Steinberg at $p$, a trivial zero appears and, using the method of Greenberg--Stevens, we calculate the first derivative of this $p$-adic $L$-function and show that it has the form predicted by a conjecture of Greenberg on trivial zeros.

Comments welcome

References in corpus (2)

• p-adic Differential Operators on Automorphic Forms on Unitary Groups
• Derivative of symmetric square p-adic L-functions via pull-back formula

Cited by in corpus (1)

• Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of $p$-adic $L$-functions