Reply to Friedlander

The Friedlander – Milnor Conjecture

Conjecture 32.1 is easily seen to be true for a torus (i.e., G G r m for some r 0), but even the simplest non-trivial case (that of G SL2 ) remains inaccessible. Guido and I published 5 papers together, all in some sense connected with this conjecture. We used the integral form GZ of a complex reductive algebraic group (which is a group scheme over Spec Z ) in order to form the group G(F) of po...

The Friedlander–iwaniec Character Sum

As we observed in [3], one can also interpret the sums S(α;β) as special cases of the correlation sums arising in our work on algebraic twists of modular forms, and we also noted that our more general results and techniques had, as special case, this theorem of Birch and Bombieri. Very recently, Y. Zhang [12, Lemma 12] made a crucial use of this estimate in his work on bounded gaps between prim...

The Authors’ Reply

The Authors’ Reply

Singularities of the wave trace for the Friedlander model

In a recent preprint, [CGJ], we showed that for the Dirichlet Laplacian ∆ on the unit disk, the wave trace Tr(eit √ ∆), which has complicated singularities on 2π − ε < t < 2π, is, on the interval 2π < t < 2π+ ε, the restriction to this interval of a C∞ function on its closure. In this paper we prove the analogue of this somewhat counter-intuitive result for the Friedlander model. The proof for ...