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arXiv · 1603.00956

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

Giovanni Rosso
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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.

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Giovanni Rosso. 2016-03-03. Derivative of the standard $p$-adic $L$-function associated with a Siegel form. https://doi.org/10.1090/tran%2F7138

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