19,339 research outputs found
Beyond endoscopy for the Rankin-Selberg L-function
We try to understand the poles of L-functions via taking a limit in a trace
formula. This technique avoids endoscopic and Kim-Shahidi methods. In
particular, we investigate the poles of the Rankin-Selberg L-function. Using
analytic number theory techniques to take this limit, we essentially get a new
proof of the analyticity of the Rankin-Selberg L-function at Along the
way we discover the convolution operation for Bessel transforms.Comment: 27 pages; accepted to Journal of Number Theor
A nonabelian trace formula
Let be an extension of number fields with simple
and nonabelian. In [G] the first named author suggested an approach to
nonsolvable base change and descent of automorphic representations of
along such an extension. Motivated by this we prove a trace
formula whose spectral side is a weighted sum over cuspidal automorphic
representations of that are isomorphic to their
-conjugates.Comment: Comments are welcom
Transients of platoons with asymmetric and different Laplacians
We consider an asymmetric control of platoons of identical vehicles with
nearest-neighbor interaction. Recent results show that if the vehicle uses
different asymmetries for position and velocity errors, the platoon has a short
transient and low overshoots. In this paper we investigate the properties of
vehicles with friction. To achieve consensus, an integral part is added to the
controller, making the vehicle a third-order system. We show that the
parameters can be chosen so that the platoon behaves as a wave equation with
different wave velocities. Simulations suggest that our system has a better
performance than other nearest-neighbor scenarios. Moreover, an
optimization-based procedure is used to find the controller properties
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