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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 16
- .......... Page(s) .......... 709
- .......... Page(s) .......... 709
- Following the idea that trees and graphs are the combinatoric versions of simply connected manifolds and Riemann surfaces we establish the vectorial Selberg trace formula for the fundamental group of a finite regular graph. As an application of this formula we study the analogue of the L functions in number theory in the context of graph theory. We obtain the meromorphic extension, the functional equation and the location of the poles of these functions.
- .......... Page(s) .......... 713
- We give two new criteria for the irreducibility of non unitary induced representations of certain semi-direct products.
- .......... Page(s) .......... 721
- .......... Page(s) .......... 721
- For manifolds carrying solutions of the homogeneous complex Monge-Ampère equation with a prescribed singularity at an isolated point, it is shown that the leaves of the Monge-Ampère foliation are extremal disks for the Kobayashi metric and distance.
- .......... Page(s) .......... 729
- .......... Page(s) .......... 729
- We give some criteria for the expression of the zeta function of an algebraic curve over a finite field. Making use of a result of Stickelberger, we show that the number of points of certain curves attains the bounds of Weil and Serre.
- MATHEMATIQUE 1987 - Tome 305 - Série I - n° 16
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