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Motivic interpretations for iterated integrals on some specific algebraic curves
Eisuke Otsuka
https://arxiv.org/abs/2404.01678 https://

Motivic interpretations for iterated integrals on some specific algebraic curves
Multiple zeta values (MZVs for short) can be represented as iterated integrals of $\mathbb{Q}$-rational algebraic differential forms on $\mathbb{P}^1(\mathbb{C})\setminus\{0, 1, \infty\}$. This interpretation allows us to consider MZVs geometrically, and this is one of the motivations for Deligne--Goncharov, Terasoma et al. to give motivic interpretations of MZVs by using the theory of mixed Tate motives and the motivic fundamental groups. In this paper, we consider the iterated integrals on …

Equicontractive weak separation property on the line does not imply convex finite type condition
Kevin G. Hare
https://arxiv.org/abs/2403.00693 https://

Equicontractive weak separation property on the line does not imply convex finite type condition
Let $\{S_1, S_2, \dots, S_n\}$ be an iterated function system on $\mathbb{R}$ with attractor $K$. It is known that if the iterated function system satisfies the weak separation property and $K = [0,1]$ then the iterated function system also satisfies the convex finite type condition. We show that the condition $K = [0,1]$ is necessary. That is, we give two examples of iterated function systems on $\mathbb{R}$ satisfying weak separation condition, and $0< \dim_H(K) < 1$ such that the IFS does no…

This https://arxiv.org/abs/2212.02606 has been replaced.
link: https://scholar.google.com/scholar?q=a

Iterated Mapping Cones on the Koszul Complex and Their Application to Complete Intersection Rings
Let $(R,\mathfrak m, \mathsf k)$ be a complete intersection local ring, $K$ be the Koszul complex on a minimal set of generators of $\mathfrak m$, and $A=H(K)$ be its homology algebra. We establish exact sequences involving direct sums of the components of $A$ and express the images of the maps of these sequences as homologies of iterated mapping cones built on $K$. As an application of this iterated mapping cone construction, we recover a minimal free resolution of the residue field $\mathsf k…

This https://arxiv.org/abs/2304.05142 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Iterated Revelation: How to Incentive Experts to Complete Incomplete Contracts
This paper examines how a decision maker might incentivize an expert to reveal novel aspects of the decision problem, expanding the set of contracts from which the decision maker can choose. The chosen contract will determine, along with the resolution of uncertainty, the payoffs to both players. I show that the set of achievable outcomes under any (incentive compatible) mechanism is characterized by a small and tractable class of iterated revelation mechanisms (IRMs). An IRM is a dynamic inter…

This https://arxiv.org/abs/2212.03119 has been replaced.
link: https://scholar.google.com/scholar?q=a

Analogues of hyperlogarithm functions on affine complex curves
For $C$ a smooth affine complex curve, there is a unique minimal subalgebra $A_C$ of the algebra $\mathcal O_{hol}(\tilde C)$ of holomorphic functions on its universal cover $\tilde C$, which is stable under all the operations $f\mapsto \int fω$, for $ω$ in the space $Ω(C)$ of regular differentials on $C$. We identify $A_C$ with the image of the iterated integration map $I_{x_0} : \mathrm{Sh}(Ω(C))\to\mathcal O_{hol}(\tilde C)$ based at any point $x_0$ of $\tilde C$ (here $\mathrm{Sh}(-)$ d…

This https://arxiv.org/abs/2208.00762 has been replaced.
link: https://scholar.google.com/scholar?q=a

Fubini's Theorem for Daniell Integrals
We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds in full generality. The results build on a density theorem on Riesz tensor products due to Fremlin, and on the Fubini-Stone Theorem.

This https://arxiv.org/abs/2404.16161 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Discrete iterated integrals and cyclic sum formulas
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for discrete iterated integrals. They imply the cyclic sum formula for multiple polylogarithms.

Discrete iterated integrals and cyclic sum formulas
Hanamichi Kawamura
https://arxiv.org/abs/2404.16161 https://arxiv.org/pdf/2404.16…

Discrete iterated integrals and cyclic sum formulas
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for discrete iterated integrals. They imply the cyclic sum formula for multiple polylogarithms.

This https://arxiv.org/abs/2208.00762 has been replaced.
link: https://scholar.google.com/scholar?q=a

Fubini's Theorem for Daniell Integrals
We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds in full generality. The results build on a density theorem on Riesz tensor products due to Fremlin, and on the Fubini-Stone Theorem.

This https://arxiv.org/abs/2403.04285 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New Multilinear Littlewood--Paley $g_λ^{*}$ Function and Commutator on weighted Lebesgue Spaces
Via the new weight function $A_{\vec p}^{θ}(φ)$, the authors introduce a new class of multilinear Littlewood--Paley $g_λ^{*}$ functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors obtain the boundedness of the multilinear commutator and multilinear iterated commutator generated by the multilinear Littlewood--Paley $g_λ^{*}$ function and the new $BMO$ function on weighted Lebesgue spaces. The results in this article include the known results in \cite{X…