Related papers: Artin-Ihara L-functions for hypergraphs

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified…

We study Artin $L$-functions on a finite $2$-dimensional complex $X_\Gamma$ arising from PGL$_3$ attached to finite-dimensional representations $\rho$ of its fundamental group. Some key properties, such as rationality, functional equation,…

We compute the Artin $L$-function of a diagonal hypersurface D_{\lambda} over a finite field associated to a character of a finite group acting on D_{\lambda} , and under some condition, express it in terms of hypergeometric functions and…

We put forward the concept of measure graphs. These are (possibly uncountable) graphs equipped with an action of a groupoid and a measure invariant under this action. Examples include finite graphs, periodic graphs, graphings and…

We consider the Ihara zeta function $\zeta(u,X//G)$ and Artin-Ihara $L$-function of the quotient graph of groups $X//G$, where $G$ is a group acting on a finite graph $X$ with trivial edge stabilizers. We determine the relationship between…

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 annihilation statement analogous to a classical conjecture of…

The Ihara expression of a weighted zeta function for a general finite digraph is given. It unifies all the Ihara expressions obtained for known zeta functions for finite digraphs. Any digraph in this paper permits multi-edges and…

For a graph $G$ of order $n$ and with eigenvalues $\lambda_1\geqslant\cdots\geqslant\lambda_n$, the HL-index $R(G)$ is defined as $R(G) ={\max}\left\{|\lambda_{\lfloor(n+1)/2\rfloor}|, |\lambda_{\lceil(n+1)/2\rceil}|\right\}.$ We show that…

The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold…

We consider the generalized weighted zeta function for a finite digraph, and show that it has the Ihara expression, a determinant expression of graph zeta functions, with a certain specified definition for inverse arcs. A finite digraph in…

We define a new weighted zeta function for a finite digraph and obtain its determinant expression called the Ihara expression. The graph zeta function is a generalization of the weighted graph zeta function introduced in previous research.…

Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of…

The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.

In this paper, using matrix techniques, we compute the Ihara-zeta function and the number of spanning trees of the join of two semi-regular bipartite graphs. Furthermore, we show that the spectrum and the zeta function of the join of two…

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 satisfied by these $L$-functions. As an application, we…

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment…

Conjecturally, almost all graphs are determined by their spectra. This problem has also been studied for variants such as the spectra of the Laplacian and signless Laplacian. Here we consider the problem of determining graphs with Ihara and…

Initially motivated by the relations between Anabelian Geometry and Artin's L-functions of the associated Galois-representations, here we study the list of zeta-functions of genus two abelian coverings of elliptic curves over finite fields.…

In various contexts, the zeta function of an object splits into a product of $L$-functions. We categorify this product formula for quadratic covers of objects in the following contexts: quadratic extensions of number fields, ramified double…

Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and Terras, Mizuno and Sato, to name just a few authors. Then, Clair and…