We introduce $L$-functions associated with characters of the Jacobian of a finite graph, as a graph-theoretic analogue of the $L$-functions arising from unramified coverings of algebraic curves. These $L$-functions are defined using the Riemann--Roch structure on the graph and extend Lorenzini's two-variable zeta function. We show that if two graphs without bridges have isomorphic Jacobians and their $L$-functions agree under the induced correspondence of characters, then their Laplacian lattices coincide. We also show that Lorenzini's zeta function is invariant under contraction of bridges, explaining the necessity of the bridge-free hypothesis in the main theorem. Finally, we give examples showing that neither the Jacobian nor the Lorenzini zeta function alone determine the Laplacian lattice.
The canonical double cover $BX$ of a graph $X$ is the direct product $X\times K_2$. A graph $X$ is stable if every automorphism of $BX$ is induced by automorphisms of $X$ and $K_2$, and unstable otherwise. We prove several asymptotic results on stable and unstable graphs. In particular, we show that the automorphism gr...
Bartłomiej Bychawski, Ademir Hujdurović, Dorde Mitrovic et al.· 0 citations
Let $C_k$ denote a cycle on $k$ vertices. Pascadi (2026) established a removal lemma for $C_{2k+1}$ in graphs with few $C_{2k}$-homomorphisms under a dense-pairs condition, using Schatten--von Neumann norms and entropy methods. We give a short proof of a version with more restrictive partition and diagonal requirements...
Motivated by conjectures arising in part from the study of class-$\mathcal{S}$ vertex algebras associated with four-dimensional supersymmetric field theories, we study multiple $q$-zeta functions attached to finite-dimensional simple Lie algebras. We prove their conjectured quasimodularity for all classical Lie algebra...
We give a complete description of the isometric isomorphisms between the $\ell^1$-crossed products of actions of discrete groups on nonempty compact Hausdorff spaces. In particular, two such crossed products are isometrically isomorphic as Banach algebras if and only if the actions are topologically isomorphic. It foll...
A $d$-set mapping is a function acting on a domain $X$ equipped with a partition into $d$ disjoint subsets. While standard functions represent $1$-set mappings, generalizations to arbitrary $d$-partite structures appear naturally across discrete mathematics. In this paper, we develop an analytic combinatorial framework...
We construct an explicit infinite family of simple two-dimensional Cayley complexes over $\mathbb{F}_2^n$ whose degree is polynomial in $n$ and whose nontrivial vertex-link eigenvalues lie in $[-\lambda,\lambda]$ for every fixed $\lambda>0$. For every fixed $d\ge2$, we also obtain an explicit infinite family of weighte...
Song-Tao Mao· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
