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Weyl Group Multiple Dirichlet SeriesType A Combinatorial Theory (AM-175)$
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Ben Brubaker, Daniel Bump, and Solomon Friedberg

Print publication date: 2011

Print ISBN-13: 9780691150659

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691150659.001.0001

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(p.96) Chapter Sixteen Concurrence
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

This chapter presents purely combinatorial results that are needed for the proof of Statement G. The motivation for these results comes from the appearance of divisibility conditions through the factor δ‎n(Σ‎; α‎) defined in (15.2) that appears in Theorems 15.3 and 15.4. According to Statement F, the sum of Λ‎subscript Greek capital letter gamma(α‎, σ‎) over an f-packet is equal to the corresponding sum of ΛΔ‎(α‎′, σ‎). In order to prove Statement F, the chapter proceeds by identifying terms in the resulting double sum that can be matched. It considers subsignatures of η‎ and concurrence as an equivalence relation.

Keywords:   concurrence, Statement G, divisibility condition, Statement F, f-packet, double sum, subsignature, equivalence relation

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