Related papers: Artin-Ihara L-functions for hypergraphs

We first describe a system of inequalities (Horn's inequalities) that characterize eigenvalues of sums of Hermitian matrices. When we apply this system for integral Hermitian matrices, one can directly test it by using Littlewood-Richardson…

Let $K/{\mathbb Q}$ be a finite Galois extension, and let $s_0\neq 1$ be a complex number. We present two new criteria for the Artin L-functions to be holomorphic at $s_0$.

A hypermap is bipartite if its set of flags can be divided into two parts A and B so that both A and B are the union of vertices, and consecutive vertices around an edge or a face are contained in alternate parts. A bipartite hypermap is…

This paper focuses on extensions of the classic Erd\H{o}s-Gallai Theorem for the set of weighted function of each edge in a graph. The weighted function of an edge $e$ of an $n$-vertex uniform hypergraph $\mathcal{H}$ is defined to a…

We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical Riemann-Hurwitz formula, study the functorial maps on Jacobians and…

The paper starts out from pseudomeasures (in the sense of Serre) which hold the arithmetic properties of the abelian $l$-adic Artin $L$-functions over totally real number fields. In order to generalize to non-abelian $l$-adic $L$-functions,…

We call a bipartite graph {\it homogeneous} if every finite partial automorphism which respects left and right can be extended to a total automorphism. A $(\kappa,{\lambda} )$ bipartite graph is a bipartite graph with left side of size…

For finite sequence $\underbar{\em d}$ of positive integers, we consider graphs that have $\underbar{\em d}$ as their list of vertex degrees, and bipartite graphs for which each part has $\underbar{\em d}$ as its list of vertex degrees. In…

We show that certain quotients of Artin L-functions have infinitely many poles. Our result follows from a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the twisted L-functions are not assumed to be entire. We do not…

We consider several examples when the extension graph admits a bipartition compatible with the action of Duflo--Serganova functors.

This is an integrated part of our Geo-Arithmetic Program. In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields by a weighted count of semi-stable bundles. Basic…

The author introduced models of linear logic known as ''Interaction Graphs'' which generalise Girard's various geometry of interaction constructions. In this work, we establish how these models essentially rely on a deep connection between…

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three applications of the explicit formula are given. First, we…

In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke's subdifferential. First of…

We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian. For XL-type Artin groups over complete graphs, we describe all possible homomorphisms with…

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given…

In this expository note we show the inception and development of the Heilbronn characters and their application to the holomorphy of quotients of Artin L-functions. Further we use arithmetic Heilbronn characters introduced by Wong, to deal…

We propose bipartite analogues of comparability and cocomparability graphs. Surprizingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex…

In this note, we introduce a family of bipartite graphs called path restricted ordered bipartite graphs and present it as an abstract generalization of some well known geometric graphs like unit distance graphs on convex point sets. In the…

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…