On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form

Details On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form

2010-07-13

arxiv.org/abs/1007.2213v1

Mathematics

Number Theory

20 pages, submitted

Scientific paper

We derive a formula for Greenberg's $L$-invariant of Tate twists of the symmetric sixth power of an ordinary non-CM cuspidal newform of weight $\geq4$, under some technical assumptions. This requires a "sufficiently rich" Galois deformation of the symmetric cube which we obtain from the symmetric cube lift to $\GSp(4)_{/\QQ}$ of Ramakrishnan--Shahidi and the Hida theory of this group developed by Tilouine--Urban. The $L$-invariant is expressed in terms of derivatives of Frobenius eigenvalues varying in the Hida family. Our result suggests that one could compute Greenberg's $L$-invariant of all symmetric powers by using appropriate functorial transfers and Hida theory on higher rank groups.

Affiliated with

Also associated with

No associations

Rating

On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Greenberg's $L$-invariant of the symmetric sixth power of an ordinary cusp form will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-119952