I was reading the two Repka papers where he computes the leading and subleading Shalika germs for $GL\_n$ and I was wondering, where are we since then? Have these germs (and the integrals) been computed somewhere? Especially if there is a reference using similar methods or something relatively simple. 


The following may be a too general question, but what do we know to date about Shalika germs? What is your viewpoint of them?



Reference for Shalika germs of GL(n)
This 2015 [paper](https://link.springer.com/chapter/10.1007/978-3-319-17987-2_3) (also on [arXiv](https://arxiv.org/abs/1412.3891)) by Frechette, Gordon, and Robson can serve as a summary of the status with pointers to the literature:



> 
> Shalika germs first appeared in the papers of Shalika and
>  Harish-Chandra. For a survey of their role in harmonic analysis on
>  $p$-adic groups we refer to the beautiful article by [Kottwitz](http://groups.claymath.org/library/proceedings/cmip04.pdf#page=405) (in particular, sections 6, 17, and 27).  
> 
>  Shalika germs, by definition, are functions on the set of regular
>  semisimple elements in a Lie algebra, yet except for those defined on
>  a few Lie algebras of small rank, their exact values elude
>  computation. Here we use a general theorem about uniform bounds for
>  motivic functions to estimate the absolute values of the Shalika germs
>  in a uniform way over all local fields of a given (sufficiently large)
>  residue characteristic.
> 
> 
> 


