The Sato-Tate law for Drinfeld modules

Details The Sato-Tate law for Drinfeld modules The Sato-Tate law for Drinfeld modules

2011-10-18

arxiv.org/abs/1110.4098v1

Mathematics

Number Theory

Scientific paper

We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module \phi defined over a field L, he constructs a continuous representation \rho_\infty : W_L \to D^* of the Weil group of L into a certain division algebra, which encodes the Sato-Tate law. When the Drinfeld module has generic characteristic and L is finitely generated, we shall describe the image of this representation up to commensurability. As an application, we give improved upper bounds for the Drinfeld module analogue of the Lang-Trotter conjecture.

Affiliated with

Also associated with

No associations

Rating

The Sato-Tate law for Drinfeld modules 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 The Sato-Tate law for Drinfeld modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Sato-Tate law for Drinfeld modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-292988