Results 21 to 30 of about 562 (207)
Lerch's $\Phi$ and the Polylogarithm at the Negative Integers
, 2021 <pre>At the negative integers, there is a simple relation between the Lerch $\Phi$ function and the polylogarithm. Starting from that relation and a formula for the polylogarithm at the negative integers known from the literature, we can deduce a ...
Jose Risomar Sousa
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A construction of the polylogarithm motive
, 2023 27 pagesClassical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial ...
Dupont, Clément, Fresán, Javier
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Cluster Algebras and Polylogarithm Relations [PDF]
, 2021 We seek to illuminate the connection between multiple polylogarithm relations and cluster algebras in two ways. First, we give a uniform description of the cluster modular group of affine and doubly extended cluster algebras.
Greenberg, Zachary
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GENERALIZED FINITE POLYLOGARITHMS [PDF]
Glasgow Mathematical Journal, 2020 AbstractWe introduce a generalization ${\rm{\pounds}}_d^{(\alpha)}(X)$ of the finite polylogarithms ${\rm{\pounds}}_d^{(0)}(X) = {{\rm{\pounds}}_d}(X) = \sum\nolimits_{k = 1}^{p - 1} {X^k}/{k^d}$ , in characteristic p, which depends on a parameter α.
Marina Avitabile, Sandro Mattarei
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International Journal of Modern Physics A, 2000 The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t). The coefficients of their expansions and their Mellin transforms
Remiddi, Ettore +1 more
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Cluster Polylogarithms I: Quadrangular Polylogarithms
, 2022 We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type $A$. We find functional equations for multiple polylogarithms which generalize equations discovered by Abel, Kummer, and Goncharov to an arbitrary weight. As an application, we prove a part of the Goncharov depth conjecture in weight six.
Matveiakin, Andrei, Rudenko, Daniil
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, 2022 Changes performance improvement of real trilogarithm Li3(double) (C, C++ and FORTRAN implementations)If you use this software, please cite it as ...
Voigt, Alexander
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Polylogarithmic Sketches for Clustering
CoRR, 2022 ICALP ...
Moses Charikar, Erik Waingarten
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Space Charge Region beyond the Abrupt Approximation
physica status solidi (b), Volume 260, Issue 11, November 2023., 2023 An analytical approximation for the potential, electrical field and charge density in a space charge (depletion) region is found. Good agreement is found with the (numerically) exact solution. The problem of the potential, electrical field and charge density in a space charge region is revisited.
Marius Grundmann
wiley +1 more source
M0, 5: Toward the Chabauty–Kim method in higher dimensions
Mathematika, Volume 69, Issue 4, Page 1011-1059, October 2023., 2023 Abstract If Z is an open subscheme of SpecZ$\operatorname{Spec}\mathbb {Z}$, X is a sufficiently nice Z‐model of a smooth curve over Q$\mathbb {Q}$, and p is a closed point of Z, the Chabauty–Kim method leads to the construction of locally analytic functions on X(Zp)$X({\mathbb {Z}_p})$ which vanish on X(Z)$X(Z)$; we call such functions “Kim functions”.
Ishai Dan‐Cohen, David Jarossay
wiley +1 more source