Daniel Vallières

activity

20172025

most citedOn the distribution of Iwasawa invariants associated to multigraphs

6 citations · 17 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2025

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

Rusiru Gambheera, Daniel Vallières

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 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 $p$ , we let $F_{p}$ and $\mathbb{Z}_{p}…

math.NT2024

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs

Rusiru Gambheera, Daniel Vallières

We initiate the study of Iwasawa theory for branched $Z_{p}$ -towers of finite connected graphs. These towers are more general than what have been studied so far, since the…

math.NT2023★ 1 cited

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

Riccardo Pengo, Daniel Vallières

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…

math.NT2022★ 3 cited

An analogue of Kida's formula in graph theory

Anwesh Ray, Daniel Vallières

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.CO2022★ 2 cited

On $Z_{ℓ}^{d}$ -towers of graphs

Sage DuBose, Daniel Vallières

Let $ℓ$ be a rational prime. We show that an analogue of a conjecture of Greenberg in graph theory holds true. More precisely, we show that when $n$ is sufficiently large, the $…

math.CO2022★ 6 cited

On the distribution of Iwasawa invariants associated to multigraphs

Cédric Dion, Antonio Lei, Anwesh Ray +1

Let $ℓ$ be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian $ℓ$ -towers of multigraphs.…

math.CO2022

The non- $ℓ$ -part of the number of spanning trees in abelian $ℓ$ -towers of multigraphs

Antonio Lei, Daniel Vallières

Let $ℓ$ and $p$ be two distinct primes. We study the $p$ -adic valuation of the number of spanning trees in an abelian $ℓ$ -tower of connected multigraphs. This is analogous to…

math.CO2021

On abelian $ℓ$ -towers of multigraphs III

Kevin J. McGown, Daniel Vallières

Let $ℓ$ be a rational prime. Previously, abelian $ℓ$ -towers of multigraphs were introduced which are analogous to $Z_{ℓ}$ -extensions of number fields. It was shown that f…

math.CO2021

On abelian $ℓ$ -towers of multigraphs II

Kevin J. McGown, Daniel Vallières

Let $ℓ$ be a rational prime. Previously, abelian $ℓ$ -towers of multigraphs were introduced which are analogous to $Z_{ℓ}$ -extensions of number fields. It was show…

math.CO2020

On abelian $ℓ$ -towers of multigraphs

Daniel Vallières

We study how the $ℓ$ -adic valuation of the number of spanning trees varies in regular abelian $ℓ$ -towers of multigraphs. We show that for an infinite family of regular abelia…

math.NT2019★ 5 cited

The special value $u = 1$ of Artin-Ihara $L$ -functions

Kyle Hammer, Thomas W. Mattman, Jonathan W. Sands +1

We study the special value $u = 1$ of Artin-Ihara $L$ -functions associated to characters of the automorphism group of abelian covers of multigraphs. In particular, we show an annihil…

math.NT2017

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 $Q$ , Rubin's c…

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

Iwasawa theory for branched Zp​-towers of finite graphs

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

An analogue of Kida's formula in graph theory

On Zℓd​-towers of graphs

On the distribution of Iwasawa invariants associated to multigraphs

The non-ℓ-part of the number of spanning trees in abelian ℓ-towers of multigraphs

On abelian ℓ-towers of multigraphs III

On abelian ℓ-towers of multigraphs II

On abelian ℓ-towers of multigraphs

The special value u=1 of Artin-Ihara L-functions