Representation zeta function of a family of maximal class groups: various exceptional cases

2026/01/05 by Shannon Ezzat
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Class (philosophy) #Function (biology) #Maximal element #Maximal function #Representation (politics)

paper · doi:10.1080/00927872.2025.2600487

openalex created_date 2026/01/05 · openalex publication_date 2026/01/05 · openalex updated_date 2026/07/25

Abstract

This paper continues Representation zeta function of a family of maximal class groups: non-exceptional primes [Citation7]. Using the explicit methods from the prequel, we compute exceptional cases of p-local representation zeta functions for finitely generated nilpotent groups Mn of maximal class. Specifically, we construct all irreducible representations of dimension pN for Mp+1 and dimension 2N for M4. Combined with previous results, this completes the classification of irreducible representations for M3 and M4 and their global representation zeta functions.

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