Daniel Vallières

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math.NT2025

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs and Ihara zeta and $L$ -functions

Rusiru Gambheera, Daniel ValliÃ¨res

We revisit the theory of Ihara $L$ -functions in the context initially studied by Bass and Hashimoto and more recently by Zakharov. In particular, we study if the Artin formalism is…

math.NT2025

An analogue of the Herbrand-Ribet theorem in graph theory

Daniel ValliÃ¨res, 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 $p$ , we let $F_{p}$ and $\mathbb{Z}_{p}…

math.NT2025

An analogue of Kida's formula in graph theory

Anwesh Ray, Daniel ValliÃ¨res

Let $ℓ$ be a rational prime and let $p : Y \to X$ be a Galois cover of finite graphs whose Galois group is a finite $ℓ$ -group. Consider a $Z_{ℓ}$ -tower above…

math.NT2024

Spanning trees in $Z$ -covers of a finite graph and Mahler measures

Riccardo Pengo, Daniel ValliÃ¨res

Using the special value at $u = 1$ of Artin-Ihara $L$ -functions, we associate to every $Z$ -cover of a finite connected graph a polynomial which we call the \emph{Ihara polyn…

Iwasawa theory for branched Zp​-towers of finite graphs and Ihara zeta and L-functions

An analogue of the Herbrand-Ribet theorem in graph theory

An analogue of Kida's formula in graph theory

Spanning trees in Z-covers of a finite graph and Mahler measures

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs and Ihara zeta and $L$ -functions

Spanning trees in $Z$ -covers of a finite graph and Mahler measures