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Koba-Nielsen local zeta functions, convex subsets, and generalized Selberg-Mehta-Macdonald and Dotsenko-Fateev-like integrals
Willem Veys, W. A. Z\'u\~niga-Galindo
https://arxiv.org/abs/2507.08120

Koba-Nielsen local zeta functions, convex subsets, and generalized Selberg-Mehta-Macdonald and Dotsenko-Fateev-like integrals
The Koba-Nielsen local zeta functions are integrals depending on several complex parameters, used to regularize the Koba-Nielsen string amplitudes. These integrals are convergent and admit meromorphic continuations in the complex parameters. In the original case, the integration is carried out on the n-dimensional Euclidean space. In this work, the integration is over a variety of (bounded or unbounded) convex subsets; the resulting integrals also admit meromorphic continuations in the complex …

On Jiang's Bounded Index Property for products of nilmanifolds
Peng Wang, Qiang Zhang
https://arxiv.org/abs/2507.06132 https://ar…

On Jiang's Bounded Index Property for products of nilmanifolds
In 2023, Zhang and Zhao presented the first examples of aspherical manifolds lacking the Bounded Index Property (BIP) for fixed points. This answered a question posed by Jiang in 1998 in the negative. In this paper, we first extend the notion of BIP to that of iterations of selfmaps (BIP$_k$), and then demonstrate BIP$_k$ for certain products $M\times N$ of nilmanifolds. Finally, we give characterizations for the Lefschetz number, the Nielsen number, and the minimal number of fixed points of se…

Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree
G. Gutin, M. A. Nielsen, A. Yeo, Y. Zhou
https://arxiv.org/abs/2507.05827

Judicious Partitions in Edge-Weighted Graphs with Bounded Maximum Weighted Degree
In this paper, we investigate bounds for the following judicious $k$-partitioning problem: Given an edge-weighted graph $G$, find a $k$-partition $(V_1,V_2,\dots ,V_k)$ of $V(G)$ such that the total weight of edges in the heaviest induced subgraph, $\max_{i=1}^k w(G[V_i])$, is minimized. In our bounds, we also take into account the weight $w(V_1,V_2,\dots,V_k)$ of the cut induced by the partition (i.e., the total weight of edges with endpoints in different parts) and show the existence of a par…

On the Dynamics of Weighted Composition Operators
Nilson C. Bernardes Jr., Antonio Bonilla, Jo\~ao V. A. Pinto
https://arxiv.org/abs/2506.04476 https://

On the Dynamics of Weighted Composition Operators
We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesàro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p(μ)$ spaces and on $C_0(Ω)$ spaces. We illustrate the general results by presenting several applications to weighted shifts on the classical sequence spaces $c_0(\mathbb{N})$, $c_0(\mathbb{Z})$, $\ell^p(\mathbb{N})$ and $\ell^p(\mathbb{Z})$ ($1 \leq p < \infty$) and to weighted translation operators on the classica…

A Novel Schwartz Space for the $\left(k,\frac{2}{n}\right)-$Generalized Fourier Transform
Nelson Faustino, Selma Negzaoui
https://arxiv.org/abs/2507.04064 …

A Novel Schwartz Space for the $\left(k,\frac{2}{n}\right)-$Generalized Fourier Transform
In this study, we introduce the generalized Schwartz space $\mathcal{S}_{k,n}(\mathbb{R})$, designed specifically for the $\left(k,\frac{2}{n}\right)-$generalized Fourier transform $\mathcal{F}_{k,n}:=\mathcal{F}_{k,\frac{2}{n}}$. We establish that $\mathcal{S}_{k,n}(\mathbb{R})$ is invariant under $\mathcal{F}_{k,n}$ and explore its principal properties in detail. Furthermore, by defining the subspace $\mathcal{D}_{k,n}(\mathbb{R})$, consisting of functions with bounded support, we show that t…