Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules for representations of orthogonal groups over F . On a global level, this local phenomenon should have implications for the structure of the value at the center of symmetry for certain L-functions of ...

As stated above, (A) is aimed at establishing a Non-Abelian Class Field Theory. The starting point here is the following classical result: Over a compact Riemann surface, a line bundle is of degree zero if and only if it is flat, i.e., induced from a representation of fundamental group of the Riemann surface. Clearly, being a bridge connecting divisor classes and fundamental groups, this result...

The aim of this note is to prove a rather explicit formula for the generating function of the Weil-Petersson volumes of the moduli spaces Mg,n of smooth npointed curves of genus g that was conjectured in [12]. E. Getzler noticed that the conecture in [12] is identical to the formulas in [5], Sect. 5, and [2], Sect. 3 and Appendix D, for the genus expansion of the free energy in Witten’s two dim...

— We construct explicitly some analytic families of étale (φ,Γ)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular ...

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne–Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Abstract We show that there are infinitely many primes of the form and . This extends work Friedlander Iwaniec showing More precisely, obtained an asymptotic formula for number this form. For sequences , we establish Type II information is too narrow aysmptotic formula, but can use Harman's sieve method to produce a lower bound correct order magnitude Estimating sums reduced counting problem so...

We prove some general estimates for exponential sums over subsets of finite fields which are definable in the language of rings. This generalizes both the classical exponential sum estimates over varieties over finite fields due to Weil, Deligne and others, and the result of Chatzidakis, van den Dries and Macintyre concerning the number of points of those definable sets. As a first application,...