arXiv Analytics

Sign in

arXiv:1603.00956 [math.NT]AbstractReferencesReviewsResources

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

Giovanni Rosso

Published 2016-03-03Version 1

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.

Related articles: Most relevant | Search more
arXiv:1903.06148 [math.NT] (Published 2019-03-14)
Lifting images of standard representations of symmetric groups
arXiv:math/0308295 [math.NT] (Published 2003-08-29)
Special cycles and derivatives of Eisenstein series
arXiv:1512.09249 [math.NT] (Published 2015-12-31)
Beyond Endoscopy via the trace formula - III: The standard representation