# Why is the simple trace formula a weaker tool than the Arthur trace formula?

What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker?

(So I do not mean weaker in the sense that the Arthur trace formula implies the simple trace formula.)

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Cyclic base change for GL(n). –  MBN Apr 24 '11 at 14:42
Also the calculation of the zeta functions of Shimura varieties. –  Alex Nov 10 '11 at 1:25

I must have missed this question a month ago, but hopefully you're still interested.

I haven't read that particular paper, but simple trace formulas have restricted test functions, which for one can only deal with representations which are supercuspidal at some place. So any theorem you prove, say about transfer of representations, needs to be restricted to functions which are supercuspidal at some finite place. In general, there may be some other restrictions also, but that depends upon the details of the simple trace formula at hand.

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Thanks a lot for this answer. I am still interested. I already thought that I will never get a proper answer to this one. –  Marc Palm May 21 '11 at 10:53
No problem. I don't read MO everyday, so I end up missing a lot of questions in my area or catching them very late. –  Kimball May 22 '11 at 18:32