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Derivative of the standard $p$-adic $L$-function associated with a Siegel form
- Publication Year :
- 2016
-
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 B\"ocherer--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.<br />Comment: Comments welcome
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1603.00956
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1090/tran/7138