2021/05/18 by Kevin J. McGown, McGown, Kevin J., Daniel Vallières +1
Mathematics · #05C50 (Primary) 11A07 #33C45 (Secondary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2105.08661
openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ℓ be a rational prime. Previously, abelian ℓ-towers of multigraphs were introduced which are analogous to ℤℓ-extensions of number fields. It was shown that for a certain class of towers of bouquets, the growth of the ℓ-part of the number of spanning trees behaves in a predictable manner (analogous to a well-known theorem of Iwasawa for ℤℓ-extensions of number fields). In this paper, we give a generalization to a broader class of regular abelian ℓ-towers of bouquets than was originally considered. To carry this out, we observe that certain shifted Chebyshev polynomials are members of a continuously parametrized family of power series with coefficients in ℤℓ and then study the special value at s=1 of the Artin-Ihara L-function ℓ-adically.