An arithmetic property of intertwining operators for p-adic groups

2021/06/02 by A. Raghuram, Raghuram, A. · 1 citation
Mathematics · #11F67 #11F70 #22E50 #22E55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2106.00960

openalex publication_date 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If one proposes to use the theory of Eisenstein cohomology to prove algebraicity results for the special values of automorphic L-functions as in my work with Harder for Rankin-Selberg L-functions, or its generalizations as in my work with Bhagwat for L-functions for orthogonal groups and independently with Krishnamurthy on Asai L-functions, then in a key step, one needs to prove that the normalised standard intertwining operator between induced representations for p-adic groups has a certain arithmetic property. The principal aim of this article is to address this particular local problem in the generality of the Langlands-Shahidi machinery. The main result of this article is invoked in some of the works mentioned above, and I expect that it will be useful in future investigations on the arithmetic properties of automorphic L-functions.

Citations

• On Certain L-Functions
• Eisenstein cohomology for orthogonal groups and the special values of L-functions for \rm GL₁ × \rm O(2n)

Cited by

• Eisenstein cohomology and congruences for the ratios of Rankin--Selberg L-functions

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