Representation zeta function of a family of maximal class groups: various exceptional cases
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.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 10
- Pages
- 3393–3407
- Publication date
- 5 January 2026
- Language
- EN