Pith. sign in

REVIEW 1 cited by

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

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1803.10273 v2 pith:T6C3AX42 submitted 2018-03-27 math.NT

classification math.NT
keywords adicmodularsiegeltrivialformsfunctionfunctionshida
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We study the derivative of the standard $p$-adic $L$-function associated with a $P$-ordinary Siegel modular form (for $P$ a parabolic subgroup of $\mathrm{GL}(n)$) when it presents a semi-stable trivial zero. This implies part of Greenberg's conjecture on the order and leading coefficient of $p$-adic $L$-functions at such trivial zero. We use the method of Greenberg-Stevens. For the construction of the improved $p$-adic $L$-function we develop Hida theory for non-cuspidal Siegel modular forms.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Iwasawa theory for $\mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation

    math.NT 2019-08 conditional novelty 8.0 of 10

    For ordinary automorphic forms on unitary groups U(r,s) over totally real fields, it proves that a rank-zero Selmer group forces the central L-value to be nonzero.

Pith tools