On a representation of the idele class group related to primes and zeros of L-functions

By R. Meyer. 2003

59 citations recorded by the source corpus.

Let K be a global field. Using natural spaces of functions on the adele ring and the idele class group of K, we construct a virtual representation of the idele class group of K whose character is equal to the Weil distribution that occurs in Andre Weil's Explicit Formula. Hence this representation encodes information about the distribution of the prime ideals of K, and it is a spectral interpretation for the poles and zeros of the L-function. It is closely related to the spectral interpretation of Alain Connes.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/994059b9833556526f0da8421649c2d7c142d745

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Citations in the corpus

Fun with $\F_1$ (2008, unknown): “Recovering the analytic endomotive 28 References 28”
Noncommutative Geometry, Quantum Fields and Motives (2007, methodology): “Our cohomological formulation here uses the same analytic tools as [224].”
The Arithmetic Site (2014, methodology): “In order to count the number of fixed points of the Frobenius action on points of (N̂×, N̄) over [0,1]max we let θuξ(x) = ξ(u−1x) be the scaling action of the idèle class group G = GL1(AQ)/GL1(Q) on functions on the adèle class space AQ/Q∗ and use the trace formula ([3, 4, 9]) in the form (ΣQ = plac”