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Iwasawa theory for branched -towers of finite graphs and Ihara zeta and -functions
Rusiru Gambheera, Daniel Vallières
We revisit the theory of Ihara -functions in the context initially studied by Bass and Hashimoto and more recently by Zakharov. In particular, we study if the Artin formalism is…
An analogue of the Herbrand-Ribet theorem in graph theory
Daniel Vallières, Chase A. Wilson
We study an analogue of the Herbrand-Ribet theorem, and its refinement by Mazur and Wiles, in graph theory. For an odd prime number , we let and $\mathbb{Z}_{p}…
Iwasawa theory for branched -towers of finite graphs
Rusiru Gambheera, Daniel Vallières
We initiate the study of Iwasawa theory for branched -towers of finite connected graphs. These towers are more general than what have been studied so far, since the…
Spanning trees in -covers of a finite graph and Mahler measures
Riccardo Pengo, Daniel Vallières
Using the special value at of Artin-Ihara -functions, we associate to every -cover of a finite connected graph a polynomial which we call the \emph{Ihara polyn…
The special value of Artin-Ihara -functions
Kyle Hammer, Thomas W. Mattman, Jonathan W. Sands +1
We study the special value of Artin-Ihara -functions associated to characters of the automorphism group of abelian covers of multigraphs. In particular, we show an annihil…
Numerical evidence for higher order Stark-type conjectures
Kevin McGown, Jonathan Sands, Daniel Vallières
We give a systematic method of providing numerical evidence for higher order Stark-type conjectures such as (in chronological order) Stark's conjecture over , Rubin's c…